Kinetically constrained models (KCMs) are able to account for many of the slow dynamical properties of glass forming systems such as dynamic heterogeneity and Stokes-Einstein breakdown using simple models with simple dynamical rules. In this thesis we study several KCMs and extend them to include fast degrees of freedom. We show how the method of Monte Carlo with absorbing Markov chains can be applied to a particular class of KCMs, the facilitated spin models, to create an efficient numerical algorithm that can speed up simulations by several orders of magnitude. Another branch of KCMs, the constrained lattice gases, are studied and new results for a version on an FCC lattice in three dimensions are presented. This model is necessary when fast dynamics are studied and dimension plays an important role. To establish how fast degrees of freedom can be introduced without changing the character of the underlying KCMs we introduce coupled Ising spins to several existing models. We find that these models can reproduce much of the fast behaviour seen in the beta-relaxation of real supercooled liquids without changing the slow behaviour that is already well described by KCMs. Lastly, by considering harmonic interactions between particles we study the relation between short-time vibrational modes and long-time relaxational dynamics in two constrained lattice gas models. We find an excess in the vibrational density of states similar to the "Boson peak" of glasses and we find a correlation between the location of these low (high) frequency vibrational modes and regions of high (low) propensity for motion in agreement with recent results from atomistic simulations.