We examine the type of information that can be obtained from Monte Carlo simulations of epitaxial growth. A basic model will be first introduced and some of the features that make it suitable for describing both atomic-scale processes and large-scale morphologies will be pointed out. The ability of this model to reproduce experimental data will then be addressed. The first example discussed will be growth on GaAs(OO1) vicinal surfaces, where the density of surface steps on the simulated surfaces reproduces quantitatively the evolution of the reflection high-energy electron diffraction (RHEED) intensity oscillations for appropriately chosen growth and diffraction conditions. This work will then be used as a basis for examining the predictions of the simulated surface morphologies on patterned substrates, based on comparisons with micro-RHEED measurements. Extensions of the basic model to more complex growth scenarios where the atomic constituents are delivered in the form of heteroatomic molecules will also be discussed.