Kinetically constrained models are simple lattice models of glasses with a dynamical frustration: a move can be performed only if some local constraints are satisfied, for example if the local density is low enough. These models have been introduced to explain on a purely dynamical ground the glass forming phenomenology. The local constraints give rise to collective dynamics leading to hierarchical and cooperative relaxation. An important issue is to understand the structure of the dynamical heterogeneity, i.e. the regions which are mobile (active) vs the regions which are blocked (inactive). The activity of the system measures the microscopic number of moves per unit time and it has been proposed as a relevant parameter to characterize glassiness. In the first part of the talk, we will review the rich dynamical behaviour displayed by the kinetically constrained models. In the second part, we will focus on the large deviations of the activity and show that it leads to a first order phase transition.