Mode selection in pulsating stars

In this review we focus on non-linear phenomena in pulsating stars: mode selection and amplitude limitation. Of many linearly excited modes, only a fraction is detected in pulsating stars. Which of them are excited, and why (the problem of mode selection), and to what amplitude (the problem of amplitude limitation) are intrinsically non-linear and still unsolved problems. Tools for studying these problems are briefly discussed and our understanding of mode selection and amplitude limitation in selected groups of self-excited pulsators is presented. We focus on classical pulsators (Cepheids and RR Lyrae stars) and main-sequence variables (δ Scuti and β Cephei stars). Directions of future studies are briefly discussed.