Models of traps and glass phenomenology

35 pages, 2 figures (not included). The two figures are available upon requestWe study various models of independent particles hopping between energy `traps\' with a density of energy barriers $\\rho(E)$, on a $d$ dimensional lattice or on a fully connected lattice. If $\\rho(E)$ decays exponentially, a true dynamical phase transition between a high temperature `liquid\' phase and a low temperature `aging\' phase occurs. More generally, however, one expects that for a large class of $\\rho(E)$, `interrupted\' aging effects appear at low enough temperatures, with an ergodic time growing faster than exponentially. The relaxation functions exhibit a characteristic shoulder, which can be fitted as stretched exponentials. A simple way of introducing interactions between the particles leads to a modified model with an effective diffusion constant in energy space, which we discuss in detail