A bus route is inherently unstable: in presence of traffic or for high passenger demands, buses fail to maintain their time-headways and so tend to bunch when the system is uncontrolled. Several bus motion models have been proposed to study the behavior of buses and evaluate regulation strategies. The ability of these models to reproduce the irregularity of bus systems comes only from stochasticity. Some recognized phenomena like a change of conditions during a day or delays at signalized intersections are ignored. This paper tries to fill this lack and provides an overview of existing dynamic bus-focused models. In a first time, commonly used deterministic and stochastic models are compared. That allows quantifying the relative influence of stochasticity of each model component on the regularity. Besides, previous works always consider routes in stationary conditions and assume that perturbations come only from stochasticity. Conversely, we show that a change of the system equilibrium leads to bus irregularity. Finally, this paper points out the inability of classical bus models to reproduce the effects of traffic signals. A refinement of travel time models is proposed to account for non- dynamic signals. Such a development could allow forecasting the bus route state in the case of Bus Rapid Transit.