We explore the influence of particle softness on the state diagram of well characterized polyelectrolyte microgel suspensions using dynamic light scattering and rheology. Upon increasing the polymer concentration, we cross successively the well defined glass and jamming transitions which delimit four different states: dilute colloidal suspension, entropic glass, jammed glass, and dense glass. Each state has a specific dynamical fingerprint dictated by two key ingredients related to particle softness: elastic contact interactions, and osmotic or steric deswelling. Soft interactions control yielding and flow of the jammed glasses. The shrinkage of the microgels makes the glass transition look smoother than in hard sphere suspensions. We quantify the relationship between the polymer concentration and the volume fraction, and show that the glass transition behaviour of soft microgels can be mapped to that of hard sphere glasses once the volume fraction is used as the control parameter.