We present an overview of the self-frequency doubling and summing lasers and we give the main optical and spectroscopic properties of the materials used in these devices. We describe a new self-doubling laser model (four and quasi-three level lasers) leading to a comparison of the different crystals (Nd;doped LNB, YAB, BNN; GdCOB and Yb-doped LNB, YAB, GdCOB) and to useful predictions on the choice of important parameters as the dopant concentration and the crystal length. (C) 2000 Elsevier Science B.V. All rights reserved.