This review provides a manual which enables the reader to perform calculations on the rate with which a biological cell can capture certain chemical compounds (ligands) which are essential to its survival and which diffuse in its environment. After a discussion of spatial diffusion and the capture of ligands by a single receptor in the cell membrane, the theory of one-stage chemoreception is developed for the general case in which the cell is spherical and arbitrary forces act between the ligand and the cell. Our method can also be applied to cells with other shapes. Next we discuss membrane diffusion and develop a theory of two-stage chemoreception. Some hydrodynamic effects are also discussed.