Electrostatics plays a crucial role in the membrane biology. Negatively charged lipids (such as PS, PA and PIP2) are subject to redistribution under the action of electrostatic forces during various signalling events. Membrane recruitment of multiple signalling proteins (such as MARCKS or Src kinase) is often maintained by positively charged polybasic domains (PD). Even though adsorption of these proteins to the cellular membrane has been extensively investigated, very little is known about how electrostatic interactions contribute to their membrane lateral dynamics. This thesis presents an investigation of the contribution of electrostatic interactions to the membrane lateral dynamics by means of novel computational tools. First, I developed a dynamic Monte-Carlo automaton that faithfully simulates lateral diffusion of the adsorbed positively charged PD of a peripheral membrane protein, as well as the dynamics of mono- (PS, PA) and polyvalent (PIP2) anionic lipids within the bilayer. This model allowed to investigate the major characteristics of protein-membrane diffusion on the uniform membrane. In agreement with earlier results, the simulations revealed the following microscopic phenomena: 1) Electrostatic lipid demixing in the vicinity of the PD; 2) PD interacts with PIP2 stronger than with monovalent lipids. On the spatially heterogeneous membrane the automaton predicted a directional drift of the PD, which was validated by a simple mean-field analytical model. The predicted phenomenon could potentially play a major role in membrane domain formation. To test this hypothesis and to investigate the membrane dynamics on larger scales I developed a continuous model, which was based on the results of the automaton simulations. The results of the continuous model and the Monte-Carlo simulations were shown to be in quantitative agreement. The continuous model allows one to simulate the electrostatic membrane dynamics on micrometer scales and can be used to describe various biologically important processes, such as endocytic cup initiation.