We report on step bunching and meandering dynamics on vicinal surfaces during MBE growth. We list four generic meandering scenarios during MBE growth: (i) when adatom desorption is significant, spatio-temporal chaos is found. When desorption is negligible three regimes are found; (ii) meandering with a wavelength which is frozen from the first stages of the instability, but whose amplitude diverges as a power law (t(1/2)); (iii) endless coarsening in the presence of elastic interactions between the steps; (iv) interrupted coarsening in presence of anisotropy. In the case of step bunching, we analyze two scenarios: (i) when desorption is important, ordered bunches appear. (ii) In the opposite limit, bunches separate, and wide terraces appear. (c) 2004 Elsevier B.V. All rights reserved.