Z-scan is a well established sensitive and accurate technique used to determine nonlinear absorption and refraction. In this paper a review-like study of the Z-scan applications for the examination of LiNbO3 crystals with different stoichiometry and with different dopants will be presented. By the extension standard Z-scan setup the cubic, the thermo-optical and the photorefractive nonlinearity can be examined. Theoretical calculations together with the measurements make possible to characterize quantitatively the thermo-optical nonlinearity and to determine the threshold dopant concentration of the photorefractive damage which is very important for nonlinear optical applications. Pure and Mg doped stoichiometric as well as congruent, and In, Hf, Zr or Y/Mg doped congruent LN samples were examined. Furthermore, a Z-scan theory based on the solution of the nonlinear paraxial wave equation, completed by the Huygens-Fresnel principle is introduced. This theory is valid for the general case, i.e. for thick samples and strong nonlinearities including both nonlinear refraction and absorption.