Numerous experimental studies of lipid vesicle adsorption on solid surfaces show that electrostatic interactions play an important role for the kinetics and end result. The latter can, e.g., be intact vesicles or supported lipid bilayers (SLB). Despite an accumulated quite large experimental data base, the understanding of the underlying processes is still poor, and mathematical models are scarce. We have developed a phenomenological model of a vesicle adsorbing on a substrate, where the charge of the Surface and the charge and polar state of the lipid headgroup can be varied. With physically reasonable assumptions and input parameters, we reproduce many key experimental observations, clarity the details of some experiments, and give predictions and suggestions for future experiments. Specifically, we have investigated the influence of different lipid mixtures (different charges of the headgroups) in the vesicle on the outcome of a vesicle adsorption event. For different mixtures of zwitterionic lipids with positive and negative lipids, we investigated whether the vesicle adsorbs or not, and-if it adsorbs-to what extent it gets deformed and when it ruptures spontaneously. Diffusion of neutral vesicles on different types of negatively charged Substrates was also simulated. The mean surface charge density of the substrate was varied, including or excluding local fluctuations in the surface charge density. The simulations are compared to available experiments. A consistent picture of the influence of different lipid mixtures in the vesicle on adsorption, and the influence of different types of substrates oil vesicle diffusion, appear as a result of the simulation data.