Granular materials are of substantial importance in many industrial and natural processes, yet their complex behaviours, ranging from mechanical properties of static packing to their dynamics, rheology and instabilities, are still poorly understood. Here we focus on the dynamics of compaction and its 'jamming' phenomena, outlining recent statistical mechanics approaches to describe it and their deep correspondence with thermal systems such as glass formers. In fact, granular media are often presented as ideal systems for studying complex relaxation towards equilibrium. Granular compaction is defined as an increase of the bulk density of a granular medium submitted to mechanical perturbation. This phenomenon, relevant in many industrial processes and widely studied by the soil mechanics community, is simple enough to be fully investigated and yet reveals all the complex nature of granular dynamics, attracting considerable attention in a broad range of disciplines ranging from chemical to physical sciences.