Computer simulations are used to investigate two features of proteins: ligand binding and ligand entry/exit. Both reveal surprising new insights into the physics of such complex systems and suggest at possible interpretations that depart from the usual paradigms. A ligand binding study using normal mode analysis suggests that, contrary to the perceived notion that ligand binding induces a tightening of the protein (as would be evidenced by a blue shift in its vibrational spectrum), there seem to be cases where ligand binding causes an increase in the entropy through a red-shift in the vibrational spectrum of the protein; this occurs in the part of the spectrum that is associated with large-scale low-frequency delocalized motions of proteins. Moreover, this increase seems to be dependent on the ability of the ligand to form hydrogen bonds within the polar cavity of the protein. This suggests an additional driving force for stabilizing complex formation. In parallel, pathways of ligand access to cavities in two proteins are mapped and it is found that, in agreement with recent interpretations of experimental data emerging from NMR studies, these pathways are characterized by a ruggedness of the energy landscape, which leads to a picture that has a physically more appealing basis than the traditional two-state paradigm normally invoked for ligand binding.