The current manifestation of the walls surrounding the city of Jerusalem does not date back to the time of Jesus or Richard I "The Lion-Hearted" (Contrary to popular opinion).
The current rampart structure was actually erected by Sultan Suleiman I somewhere around the mid-16th century. The fortifications only contain the Old City, while expansion of the New City has grown around it since the creation of the State of Israel in 1948. This expansion has been focused predominantly to the west and south of the old city walls
One function of the fortification system, the gates (moving clockwise from the north: Herod's, Lion's, Dung, Zion, Jaffa, and Damascus) were likely in existance during the time of Jesus (as perhaps indicated by his path of exit from the city via the "Dung Gate"), but certainly not in their current form. These gates were likely rebuilt when Suleiman rebuilt the rest of the wall structure.
The walls themselves make for an excellent way to view both sides of the city, old and new. If you ever make your way to Jerusalem be sure to climb up the steps and take a peak at your surroundings (especially in around daybreak or nightfall).