This review deals with the problem of selective detection of single atoms by laser radiaton. It begins with a classification of the detection methods (fluorescence, photoionization, deflection), discusses detection conditions (atomic vapor, atomic beam, buffer gas), and gives estimates of the parameters of laser radiation ensuring effective detection. Next, a detailed comparision is made of each of the detection methods. It is shown that in the fluorescence method the maximum efficiency of the detection process is achieved for cyclic interaction of atoms with laser radiation. In the photoionization method the most suitable technique is multistage photoionization of atoms by laser radiation. The highest ionization selectivity and a high efficiency are obtained by multistage excitation of an atom either to a Rydberg state followed by ionization with an electric field pulse or to a narrow autoionizing state with a large excitation cross section. Both these techniques are considered from the point of view of the sources of background and ways of discriminating against it, detection selectivity, and absolute sensitivity; the experimental results are analyzed. In discussing the deflection method consideration is given to deflection of an atom in a magnetic field after excitation with laser radiation and to deflection of atoms by resonant optical pressure. The review concludes with a brief discussion of the prospective applications of these detection methods in nuclear physics, atomic physics, and chemistry.