A network of dynamical systems (say, neurons) driven by a fluctuating time-dependent signal is said to be reliable if, upon repeated presentations of the same signal, it gives essentially the same response each time. As a system's degree of reliability may constrain its ability to encode and transmit information, a natural question is how network conditions affect reliability; this question is of interest in e.g. computational neuroscience. In this talk, I will report on a body of work aimed at discovering network conditions and dynamical mechanisms that affect the reliability of networks, within a class of idealized neural network models. I will discuss a general condition for reliability, and (time permitting) survey some specific mechanisms for reliable and unreliable behavior in concrete models and how they are manifested on different scales.