One of the major challenges that autonomous cars are facing today is driving in urban environments. To make it a reality, autonomous vehicles require the ability to communicate with other road users and understand their intentions. Such interactions are essential between the vehicles and pedestrians as the most vulnerable road users. Understanding pedestrian behavior, however, is not intuitive and depends on various factors such as demographics of the pedestrians, traffic dynamics, environmental conditions, etc. In this paper, we identify these factors by surveying pedestrian behavior studies, both the classical works on pedestrian-driver interaction and the modern ones that involve autonomous vehicles. To this end, we will discuss various methods of studying pedestrian behavior, and analyze how the factors identified in the literature are interrelated. We will also review the practical applications aimed at solving the interaction problem including design approaches for autonomous vehicles that communicate with pedestrians and visual perception and reasoning algorithms tailored to understanding pedestrian intention. Based on our findings, we will discuss the open problems and propose future research directions.