NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. The application of Monte-Carlo simulations to study thermally excited time-dependent phenomena is examined. The diffusion coefficient and the exponent for domain growth for a square lattice gas experiencing equal and repulsive nearest-neighbor and next-nearest-neighbor interactions are calculated for three different dynamics: Kawasaki; Metropolis and energy-barrier. All three dynamics satisfy detailed balance, but the diffusion coefficient is found to show a different temperature dependence for each. The growth exponents for Kawasaki and energy-barrier dynamics are in close agreement, and larger than that for Metropolis dynamics. This difference arises because the domain sizes reached were not sufficiently large. In further Monte-Carlo simulations of the same lattice gas model using dynamics which allow precursor-mediated migration, the growth exponent of fourfold degenerate ordered (2x1) domains on a square lattice is found to be 1/2. If the growth law is written as [...], A is found to be proportional to [...], where D is the diffusion coefficient of the adsorbed particle. Kawasaki dynamics simulations at zero temperature are performed for the growth of [...] domains on a triangular lattice. The results show that the low temperature behavior is markedly dependent upon the details of the lateral interactions and the range of the particle hops. This latter result demonstrates the strong influence of a precursor state on growth kinetics. Monte-Carlo analysis of molecular beam reflectivity measurements of the probability of molecular adsorption of ethane on the Ir(110)-(1x2) surface shows that a precursor state can also be rather important in adsorption. We show that the experimental data can be explained by adsorption occurring in two channels: direct and precursor-mediated. In this case the precursor is an ethane molecule trapped in a second layer on top of the first layer of molecularly adsorbed ethane. From the simulations we were also able to calculate the energy barriers for diffusion and desorption of an ethane molecule in the precursor state. Monte-Carlo simulations of a Langmuir-Hinshelwood reaction between two interacting species were also performed. The parametrization of the reaction rate coefficient that is implicit in an Arrhenius plot is examined. It is shown that the effective energy barrier and preexponential factor obtained from an Arrhenius plot show strong compensation when the overlayer configuration is strongly temperature dependent. This can explain the anomalously high reaction or desorption preexponential factors observed for some adsorbed systems. It is also shown that a Langmuir-Hinshelwood reaction occurring between two species, even when they are non-interacting, can lead to configurational effects. Compact 'islands' consisting solely of either species A or species B are observed in simulations. An order parameter which allows an analogy between the reacting system and magnetic systems to be drawn is defined. The reactivity of the catalyst surface is inversely proportional to the 'island' size.