Proteins are dynamic macromolecules and their dynamics is deemed necessary for their functions. The dynamical properties of proteins can be studied through the temperature dependence of their equilibrium fluctuations: Elastic Neutron Scattering (ENS) is perhaps the most relevant experimental technique to this purpose but other classical techniques like e.g. Fourier Transform Infrared Spectroscopy (FTIR) spectroscopy can give relevant, complementary, information. In this talk I will discuss recent data on the so-called Protein Dynamical Transition (PDT: i.e. an abrupt increase in the protein mean square fluctuations occurring at about 210K in hydrated protein powders) and on its dependence upon hydration solvent and pressure. Data obtained with ENS –which gives the mean square displacements of non-exchangeable hydrogen atoms of the protein and is therefore particularly sensitive to side chain motions- will be compared with FTIR data in the Amide region -which is sensitive mainly to the properties of the backbone atoms of the protein-, thus obtaining information on molecular details of the involved protein motions. The pressure dependence of the PDT, in the range 20 bar – 5 kbar, will also be investigated and the effects of pressure on the energy landscape of the protein (height and roughness of the energy barriers) will be discussed.