Using light scattering (multispeckle DLS) and rheological (dynamic frequency sweep, creep and start-up in shear) techniques, we investigate the slow dynamics of concentrated suspensions of star polymers, a model soft colloidal system with tunable interactions. We focus on the transition to the glassy regime which, depending on the suspending medium used, can be reached by increasing the number concentration or the temperature. We observe a rich dynamics associated with this reversible liquid to solid transition. The rheology changes from viscoelastic to viscoplastic rather gradually, and very long stress transients are detected. At the same time, the appearance of slow relaxation process in the intermediate scattering function is evidenced, which appears to be responsible for the macroscopic immobilization of the system. This relaxation process exhibits a logarithmic decay over 3 decades in time with extremely slow kinetics (ageing); the latter is also manifested in a second ultraslow process in start-up experiments. The above relaxation process decays gradually from stretched to logarithmic manner at high temperatures. We attempt at comparing this systematic information with the analogue experimental evidence from hard sphere suspensions, attributing the similarities to universality in behavior, the differences to the nature of the interactions, and leaving several open questions for further research.