Automatic sleep staging has remained a constant challenge over the years due to scientific and economic reasons. Rapid eye movement (REM) sleep recognition is a most critical subtask for these procedures. Because the physiological meaning of REM sleep is still an open question and the identification depends on the coordinated behavior of three biological signals, the present definition still has to be considered preliminary and arbitrary to some extent. Three neural network-based algorithms for automatic REM sleep recognition are reviewed herein. All of them rely on a single EEG channel as input signal, but differ in the preprocessing method. The results are encouraging but might be improved with respect to the interrater concordance rate. Applying nonlinear measures could not reduce the errors in our study. Other biological parameters are discussed that might help to improve the results.