The motility of living eukaryotic cells is a complex process driven mainly by polymerization and depolymerization of actin filaments underneath the plasmatic membrane (actin cytoskeleton). However, the exact mechanisms through which cells are able to control and employ 'actin-generated' mechanical forces, in order to change shape and move in a well-organized and coordinated way, are not quite established. Here, we summarize the experimental results obtained by our research group during recent years in studying the motion of living cells, such as macrophages and erythrocytes. By using our recently developed defocusing microscopy technique, which allows quantitative analysis of membrane surface dynamics of living cells using a simple bright-field optical microscope, we were able to analyse morphological and dynamical parameters of membrane ruffles and small membrane fluctuations, study the process of phagocytosis and also measure values for cell refractive index, membrane bending modulus and cell viscosity. Although many questions still remain unanswered, our data seem to corroborate some aspects of recent physical models of cell membranes and motility.