The only known systems that exhibit truly intelligent, autonomous behavior are biological. If we wish to build machines that are capable of such behavior, then it makes sense to learn as much as we can about how these systems work. Inspiration is a good starting point, but real progress will require gaining a more solid understanding of the principles of information processing at work in nervous systems. Here I will focus on five areas of investigation that I believe will be especially fruitful: 1) the study of perception and cognition in tiny nervous systems such as wasps and jumping spiders, 2) developing good computational models of nonlinear signal integration in dendritic trees, 3) the use of sparse, overcomplete representations of sensory input, 4) understanding the computational role of feedback in neural systems, and 5) the use of active sensing systems for acquiring information about the world.