Rome did not have a written constitution as the United States or Australia do. It did not even appear to have a Westminster style one such as Britain's or Tasmania's which exists across multiple non-contiguous acts. It seems to be purely a mix of convention and tradition. Which was probably why it was easy for Sulla, Caesar and Augustus to subvert it.
We mainly know the Senate as the Roman political body, but prior to 510BC Rome was ruled by a monarch until (King) Tarquin was run out of town. This led to a fear of unitary or supreme power and Roman political institutions established themselves to stop such an outcome. What replaced it was effectively a Senate led oligarchy. For most of Rome's early history approximately twenty families dominated the Senate and it was rare that outsiders were able to establish themselves sufficiently to become Senators - Cicero was one of those rarities.
Since Montesquieu it has been firmly established that the three branches of government are executive, legislative and judicial. The Roman system does not really fit into those categories; the Senate being problematic again; but the Roman institutions are near enough that modern Australians would recognize executive, legislative and judicial functions in the Roman political bodies.
The main Executive position was the Consul. Rome solved the issue of absolute power and sovereignty in this position by electing two Consuls each term who would alternate month to month. A Consul's term was twelve months and they could not be re-elected Consul after serving in the position.
This pluralistic or power-sharing aspect of Roman politics may have been why would-be emperors such as Caesar, Augustus, Antony, Pompey, Crassus, Lepodus etc were happy dividing the Roman Empire up and ruling it as
triumvirates - however transitory the arrangements were; ie Caesar crushed Pompey, and Augustus crushed Antony.
After a Consul's term was up they became a Proconsul and were sent off to govern a province such as Spain, Africa, Macedonia, Cisalpine Gaul etc. Anywhere that was far away from Rome. For the Proconsuls there was the added advantage of being able to extort the provinces for money as Roman elections were usually quite expensive - what with all the bribing and whatnot.
There was no civil service or bureaucracy in Roman times, that was a technology that was invented during English and French dominance in the 1700s as they required organisational technologies to support their highly militaristic and capital intensive war machines; such as a navy and continental army.
Roman politicians carried the burden of the civil service as they would take their own people with them to their appointed position and the cost tended to be defrayed by the wealth that a Roman could make in such a position. There was also no tax department either; especially not in the provinces. Tax collection was sold off, or bidded for. Tax Farmers were a wealthy and politically influential special interest group that rivalled the merchants for the ears of Roman politicians.
The Roman system carried checks and balances everywhere, and achieving the position of Consul required serving in several political positions first. An aspiring Roman public figure had to first serve as a Quaester. These were like provincial tax collectors. Cicero, for instance, served his period as Quaester on Sicily.
After serving as a Quaester the individual was eligible to become an Aedile of which they were only four in Rome. This wasn't absolutely necessary to become a Consul as it was an expensive position to hold. Most of the civic improvements came out of the Aedile's own pocket. Crassus apparently made the comment in his later life that you "Weren't rich unless you could afford to pay an army." Which gives an idea of how oligarchic the Roman system was. Only the Bill Gates, Warren Buffet's etc of Rome could afford politics; George Bush would be too poor to be part of the Roman oligarchy.
The final position before Consulship was as a Praetor. This position held real executive power as they executed the law in provinces and stood as judges. The Roman judicial system is different to our form. For instance all cases, criminal or civil, were brought by individuals against another. Again, there was no civil service, no police force, and no real penitential system. So most decisions were fiscal in nature. Capital punishment was extremely rare even in times of emergency.
The Roman lawyers used to act like TV attorneys. They would be the interviewer, the detective, the collector of evidence and then would represent their client in the Forum, defending their case with a speech full of rhetoric, innuendo and facts. This would be done infront of a public audience, who would react to the speech with cheers and boos. It is hard to believe that mob justice didn't have an influence on Roman law cases in such an environment.
The Senate was an unusual body. It wasn't really legislative, as it didn't make laws, however it controlled money supply and made policy. It also reviewed any legislation that came from the Assemblies, effectively giving it the yay or nay. Probably the closest analogy to their function in a modern democracy is the committee system in the Australia. But even that is a bad analogy.
Senators were appointed for life, and because of the high turnover of Consuls and their power-sharing requirements, the real power of Rome was in the Senate. It dominated what an executive could do, what was political achievable in the system, and how policy was conducted. It was a permanent institution, consequently it was very conservative in its political operation.
The Consuls and Tribunes were far more temporary institutions and it is a not a surprise that most radicalism came from those bodies such as Sulla, Caesar and Augustus. Than again Caesar during his period as dictator/tyrant managed to appoint so many Senators that it became a body pliant to his executive will.
The other positions in the Roman executive were the Censors and the Tribunes. The Censors were like public servants, they conducted administrative functions such as keeping the census up to date, enrolling citizens, purging the Senate of deadwood (!). There were only two Censors and the individual had to have been a Consul to become one.
The final position is the Tribune. This position came into being when the people (
plebs) removed their labor from Rome in 493BC and basically conducted a strike over debt relief by camping en-masse on a nearby hill. To placate the plebs and have them return to Rome a voice of the people, the Tribune, was established. The Tribunes could propose legislation and could convene a Senate meeting to respond to the concerns of the people, but their main power was the veto.
The veto was the ultimate Roman power of check and balance. Consuls could veto, Praetors could veto and Tribunes could veto. The veto was final too, and only required one Consul, Praetor or Tribune to shoot down a proposal. It seems the idea was that it covered an executive veto, a kind-of judicial veto and a popular veto to place a check on absolute power.
One of the criticisms of the Roman system was that this overlapping check and balance created stasis in the system such that good governance could not occur; and consequently a unitary executive was required to come in and plow through these obstructions to government. When Caesar established himself as dictator he basically did an end-run around these checks and balances, however he made the other positions weak or pliant to his executive will. Augustus did similar. So this is not necessarily a good argument.
There is an argument that all the overlapping made the constitution and conventions difficult to change. Which was an issue successive Roman reformers discovered. The loophole in the Roman constitution was the position of dictator, and this is what reformers such as Sulla, Caesar and Augustus used to get around the Senate. The Dictator was a formal position, established through law, where a Consul had supreme power for six months.
This law was enacted through the Final Act which the Senate would vote into being. This would establish
tumultus where civil law falls down and laws becomes the arbitrary whim of the Dictator. This is where the state of emergency and state of exception, as well as Agamben's work on
homo sacer come from.
Roman politics were militaristic. Consuls and Senators were expected to be generals as much as they were required to be politicians. A quick method for an aspiring Roman politician to become a public figure was to be a successful general. For instance Pompey rose to public prominence through raising an army illegally and leading it to success during a civil war. He was twenty-three when he did that.
There were two legislative bodies in the Roman system during Cicero's time, or its most powerful age. There was the Centuriate Assembly which was a military body, and the General Assembly which was tribally based and called
comitia tributa in Latin. The General Assembly approved bills, but it didn't debate them. It could also declare war. The General Assembly was territorially based rather than the oligarchic nature of the Senate which only included the wealthy families. But all democracy was constrained in Rome by transport and communications.
Enfranchisement in Rome was for male citizens and elections were held in Rome, so only those that were within travel distance of Rome could vote. Given the size of the Roman Empire, and the lack of a representative system of government, this meant that citizens in Rome wielded a great deal of power over the politics of the Empire.
cam

I am an Australian living in the United States as a permanent resident.
I am a software developer by trade and mostly work in Java and jump between middleware and front end.
I originally worked in the New York area of the United States in telecommunications before moving to Washington DC and
working in a mix of telecommunications, energy and ITS. I started my own software company before heading out to
Arizona and working with Shutterfly. Since then I have joined a startup in the Phoenix area and am thoroughly enjoying myself.
I do a lot of photography which I post on this website, but also on flickr. I have a photo-journalistic website which lists
the modernist and contemporary restaurants in phoenix. I have a site on the
Australian Flying Corps [AFC] which has been around since the 1990s and which I unfortunately
lost the .org URL to during a life event; however, it is under the
www.australianflyingcorps.com URL now.
The AFC website has gone through several iterations since the 90s and the two most recent are
Australian Flying Corps Archives(2004-2002) and
Australian Flying Corps Archives(2002-1999) which are good places to start.