Modern silicon integrated circuits and vertebrate nervous systems are the two of the most compact, complex information processing systems presently known. Within these two classes of system, most information processing is handled in discrete (ie digital) form, but analog components appear in both systems as well. In silicon, wireless communication circuits are typically implemented using analog signal processing. In the central nervous system, the retina plays a similar role of interfacing with the physical world, and also employs analog circuitry. In both cases the primary problem is performing analog operations with low power and high robustness in spite of imperfect circuit components. In this dissertation presents transistor circuits that make up a very low power radio, and neural circuits that have been extracted from direct measurement of retinal neurons in the rabbit retina. Running at a carrier frequency of 900MHz, the radio described here was shown to communicate up to 100 kilobits per second at ranges of 16 meters or more while consuming 1.3mW in transmit mode and 1.2mW in receive. The whole design only requires 4 external components at a cost of less than 1 dollar. Power reduction was achieved by stacking circuits to make maximum use of battery voltage, and using a single high quality inductor to resonate out capacitance on the inputs of each RF block. Simple passive switching mixers were also employed, improving the linearity of the system and permitting demodulation of 1.0 picowatt wanted signals in the face of interfering signals as large as 100 uW. This design also incorporated a new type of current mirror that with just three additional transistors reduces the voltage headroom by more than a factor of 2 with very little cost in terms of current or die area. The circuits presented here represented a new record in terms of performance at low power. In the retina, bipolar cells are the primary analog feed-forward cells, but also participate in feedback networks thought to generate diverse signaling pathways. Strikingly, while there are at least 10 morphologically distinct classes of bipolar cell, electrophysiological measurements of these cells only showed 4 distinct types of inhibitory feedback. The most common type of inhibition, which we call crossover inhibition, acts between the ON and OFF systems, causing each to suppress the other. This type of inhibition also was evident in amacrine and ganglion cells, such that it makes up the most common form of inhibition in the inner retina. Chapter 5 shows that this class of inhibition acts to suppress even-order (rectifying) nonlinearity, which is introduced by most synapses in the retina. This effect is analogous to the way differential circuits used in radios suppress even order nonlinearity in receiver circuits. Pharmacological manipulation shows that the linear outputs of the retina, long considered the default pathways (as opposed to special-function nonlinear outputs) are in fact only linear because of the activity of crossover inhibition suppressing their nonlinearity. All of these effects have been verified using both direct patch-clamp recordings and computer simulations. Preliminary analysis also indicates that the precise asymmetry seen in bipolar and amacrine inhibition yields a circuit topology that is optimally stable and resistant to system-wide shifts in excitability. This work elucidates the inhibitory circuitry that maintains linearity in the primary visual pathways in mammals, and further demonstrates how the retina maintains its robust functionality in the face of inevitable variability in the components of the system. Thus, as in low power radios, the primary problem to be solved in low power analog circuits in the retina is one of reliability in the face of unreliable physical components.