This review describes bolometric detectors for infrared and millimeter waves. The introduction sketches the history of modern bolometers, indicates how they fit into the more general class of thermal detectors, and describes the types of applications for which they are the optimum solution. Section I is a tutorial introduction to the elementary theories of bolometer response, of thermal radiation, and of bolometer noise. Important results are derived from the laws of thermal physics in the simplest possible way. The more rigorous theories of bolometer response and noise that are required for quantitative understanding and optimization are then summarized. This material is intended to provide the background required by workers who wish to choose the appropriate bolometer technology for a given measurement, or to evaluate a novel technology. Section II, then describes the various components of an efficient bolometer and gives details of the fabrication and performance of modern bolometers. This discussion focuses on composite bolometers with semiconducting thermometers for operation at and below liquid helium temperatures. The tradeoffs involved in using superconducting thermometers at low temperatures are discussed. Finally, a discussion is given of bolometers for operation at liquid nitrogen temperature which use the new high-Tc superconductors as thermometers.