There are several known constructions of equilibrium states for Hölder continuous potentials in the context of both subshifts of finite type and uniformly hyperbolic systems. In this talk I will present another method of building such measures, formulated in the unified and more general setting of Smale spaces. This simultaneously extends our previous work for hyperbolic attractors (modelled after Sinai's classical approach for SRB-measures) and gives a new and original construction of equilibrium states for subshifts of finite type. This is joint work with Mark Pollicott.