  The mobility of membrane proteins controls many biological functions. The
application of the model of Saffman and Delbr\"uck to the diffusion of membrane
proteins does not account for all the experimental measurements. These
discrepancies have triggered a lot of studies on the role of the mechanical
factors in the mobility. After a short review of the Saffman and Delbr\"uck
model and of some key experiments, we explore the various ways to incorporate
the effects of the different mechanical factors. Our approach focuses on the
coupling of the protein to the membrane, which is the central element in the
modelling. We present a general, polaron-like model, its recent application to
the mobility of a curvature sensitive protein, and its various extensions to
other couplings that may be relevant in future experiments.
