The thousands of inputs a single neuronal cell receives can interact in complex ways that depend on their spatial arrangement and on the biophysical properties of their respective dendrites. For example, operations such as coincidence detection, pattern recognition, input comparison, and simple logical functions can be carried out locally within and across individual branches of a dendritic tree. In this talk, we will present the hypothesis that the brain leverages these fundamental integrative operations within dendrites to increase the processing power and efficiency of neural computation. We will focus on sensory processing and spatial navigation, with the goal of understanding the mechanistic basis of these brain functions.