Second-order macroscopic models and most car-following models are able to reproduce traffic waves or other observed instabilities of traffic flow. After an intuitive introduction, we define the relevant stability concepts such as local instability, convective and absolute string and flow instability, or Ljapunov and asymptotic stability. We give general analytic criteria for the occurrence of these instabilities for microscopic and macroscopic models. For microscopic models, we compare the approaches via Fourier analysis and transfer functions. The formulation is more comprehensive than the various accounts in the specialized literature and can be evaluated for any traffic flow model with a well-defined acceleration function, and also for models with explicit time delays or considering several vehicles ahead (multi-anticipation) or one in the back. The stability criteria allow us to characterize the influencing factors of traffic flow instabilities and answer the question of if, and in which way, the driving behavior (or advanced driver-assistance systems) influence traffic flow stability.