Single-molecule observation, characterization and manipulation techniques have recently come to the forefront of several research domains spanning chemistry, biology and physics. Due to the exquisite sensitivity, specificity, and unmasking of ensemble averaging, single-molecule fluorescence imaging and spectroscopy have become, in a short period of time, important tools in cell biology, biochemistry and biophysics. These methods led to new ways of thinking about biological processes such as viral infection, receptor diffusion and oligomerization, cellular signaling, protein-protein or protein-nucleic acid interactions, and molecular machines. Such achievements require a combination of several factors to be met, among which detector sensitivity and bandwidth are crucial. We examine here the needed performance of photodetectors used in these types of experiments, the current state of the art for different categories of detectors, and actual and future developments of single-photon counting detectors for single-molecule imaging and spectroscopy.