Materials consisting of concentrated soft particles closely packed in an amorphous state are found in many day-to-day systems like pastes, tissues or emulsions. The rheological properties of these systems are usually characterized by slow relaxations and by the existence of a yield stress, among other signatures, reflecting the existence of glassy dynamics. A key point in soft condensed matter is to establish a link between the macroscopic properties and the microscopic structure and dynamics of these glassy systems. We show that suspensions of microgel particles are a flexible model system sharing some of the fundamental characteristics of molecular glasses. Here, the particle size depends on external variables, such as temperature and pH, and on the degree of network cross-linking. Size can also be tuned with concentration above random close packing, since microgels are then forced to shrink to fit in the given volume. By changing any of these parameters the system shows a rich behavior. In particular, it undergoes glass-like to liquid-like to gel-like dynamics as function of temperature; this is shown with bulk rheological measurements and with the use of dynamic light scattering and confocal imaging to access the system local dynamics.