The Roman Senate was one of the longest politics institutions on our history. Created before the first Rome emperor goes to the throne (753 bC), it Survived to the Roman Emperor fall, Roman Republic fall and Occident Roman Emperor fall. Its power apices was at Republic time (509 - 27 bC). Even nowadays the Roman Senate influences parliaments on many countries.
1) Physical Constructions - The senatum was divided into three distinct sessions, knew as Right, Left and Center. A lot of parliaments today still uses this model to dispose your parliamentarians. It's beautiful... Right, Left, Center... groups disposed harmonically!
2) The Senate just has really power into a Republic. With the Republic fall the senate had lost its power on the Emperor. In this time they didn't have much to do, so they got together to play football games, drink some beer (in fact only barbarians used to drink beer. Romans used to drink wine with sweet fruits smell, picked by boys in transparent togas... a totally hetero thing :P ), play some cards, etc.
3) In the Roman Senate was a person (princeps senatum) whose rules the party! In the actual senate and parliaments we still have this person whose open the sessions, command the tribune, does enthusiastic preachments and close the sessions.
4) The Senate used to elect and overthrown kings. This still happens at many countries where the stronger vote is made by the senators and parliamentarians. The overthrown is much more difficult today. On Rome normally they used to kill the Emperor or King. Much more easy!
5) And since they were not paid, individuals usually sought to become senators only if they were independently wealthy. Very different from today when they become wealthy AFTER become a Senator or Parliamentary. It's an amazing thing! Once they already have a occupation full of privileges and regales, they also still are paid (a lot!) to "represent" you! The only common thing was that they couldn't engage in banking or any form of public contract. Indeed they still could get (and still can!) those fantastic deals between family companies and friend's companies and every body (family and friends) get happy!