This paper briefly reviews recent results of extensive Monte Carlo simulations for the glass transition of polymer melts. The simulation used the bond-fluctuation model, a lattice model, which exhibits glassy behaviour due to the development of a competition between packing constraints and chain stiffening at low temperatures. For this model static and dynamic properties were analysed, such as the influence of the cooling rate and of the chain length on the glass transition temperature, physical aging effects, the time-dependences of various mean-square displacements and structural relaxation functions and the temperature-dependences of structural relaxation times and of the diffusion coefficient. Besides an outline of these results we discuss in some detail a quantitative comparison between the incoherent intermediate scattering function and the extended mode-coupling theory and between the entropy of the melt and the Gibbs - Di Marzio theory.