The nervous system is a surprisingly noisy place. For example, if one presents the exact same stimulus to an animal many times, and records the activities of their sensory neurons, those neural responses typically show high levels of trial-to-trial variability. At the same time, we have the experience of having robust thoughts and perceptions. How do our brains generate this robustness from systems of individually unreliable components? In my talk, I will discuss three major circuit mechanisms that have been advanced by my research program. First, I will discuss a mechanism through which the nervous system can learn the statistical structure of the stimuli that it typically experiences. This knowledge allows for the nervous system to make educated guesses about the most likely stimulus presented, even when that stimulus is corrupted by noise. The de-noising process works best when the stimuli, and the noise that corrupts them, have different statistical structures. This motivates the second principle that I will discuss, namely that the peripheral nervous system can shape its noise statistics such that the noise only minimally interferes with the transmission of information about the external world. In particular, I will present a circuit mechanism through which the retina appears to perform this noise shaping. Finally, I will confront the fact that neural systems (like those involved in memory) must typically maintain stable representations even while the responses of individual neurons evolve dynamically over time, and are noisy. Using modern data-science tools, I will illustrate a novel mechanism through which the hippocampus appears to solve this problem. In addition to the importance of these circuit mechanisms for basic science, I will highlight in my talk the implications of my work for the creation of useful biomimetic technologies.