Time-of-flight (ToF) sensors offer a cost-effective and realtime solution to the problem of three-dimensional (3-D) imaging-a theme that has revolutionized our sceneunderstanding capabilities and is a topic of contemporary interest across many areas of science and engineering. The goal of this tutorial-style article is to provide a thorough understanding of ToF imaging systems from a signal processing perspective that is useful to all application areas. Starting with a brief history of the ToF principle, we describe the mathematical basics of the ToF image-formation process, for both time- and frequency-domain, present an overview of important results within the topic, and discuss contemporary challenges where this emerging area can benefit from the signal processing community. In particular, we examine case studies where inverse problems in ToF imaging are coupled with signal processing theory and methods, such as sampling theory, system identification, and spectral estimation, among others. Through this exposition, we hope to establish that ToF sensors are more than just depth sensors; depth information may be used to encode other forms of physical parameters, such as, the fluorescence lifetime of a biosample or the diffusion coefficient of turbid/scattering medium. The MATLAB scripts and ToF sensor data used for reproducing figures in this article are available via the author?s webpage: http://www.mit.edu/~ayush/Code.