High transparency, low light-scattering, and low autofluorescence of mammalian tissues in the near-infrared (NIR) spectral range (~650-900 nm) open a possibility for in vivo imaging of biological processes at the micro- and macroscales to address basic and applied problems in biology and biomedicine. Recently, probes that absorb and fluoresce in the NIR optical range have been engineered using bacterial phytochromes - natural NIR light-absorbing photoreceptors that regulate metabolism in bacteria. Since the chromophore in all these proteins is biliverdin, a natural product of heme catabolism in mammalian cells, they can be used as genetically encoded fluorescent probes, similarly to GFP-like fluorescent proteins. In this review, we discuss photophysical and biochemical properties of NIR fluorescent proteins, reporters, and biosensors and analyze their characteristics required for expression of these molecules in mammalian cells. Structural features and molecular engineering of NIR fluorescent probes are discussed. Applications of NIR fluorescent proteins and biosensors for studies of molecular processes in cells, as well as for tissue and organ visualization in whole-body imaging in vivo, are described. We specifically focus on the use of NIR fluorescent probes in advanced imaging technologies that combine fluorescence and bioluminescence methods with photoacoustic tomography.