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This talk concerns the reliability of large networks of pulse-coupled oscillators in response to fluctuating stimuli. Reliability means that a stimulus elicits essentially identical responses upon repeated presentations; whether a network is reliable can impact its ability to encode information via the precise timing of spikes. Focusing on a class of layered network architectures, I will discuss the problem on two scales: neuronal reliability, which concerns the repeatability of spike times of individual oscillators embedded within a network, and pooled-response reliability, which addresses the repeatability of the total output from the network. Through a combination of qualitative theory and systematic numerical studies, it will be shown that individual embedded oscillators can be reliable or unreliable depending on network conditions, whereas pooled responses of sufficiently large networks are mostly reliable. I will also discuss the effects of noise, and show that some types affect reliability more seriously than others.