In this article, we summarize the knowledge in the field of irreversible deposition processes of large molecules or colloidal particles on solid surfaces. An irreversible adsorption process is defined as a process in which, once adsorbed, a particle can neither diffuse along, nor desorb from the surface. We first introduce the basic tools used in these studies, one of the most important being the concept of available surface function. General results relative to these processes are then presented. We discuss, in particular, the connection between the reduced variance of the number density fluctuations of adsorbed particles and the available surface function. We then review the main models which were introduced in the literature to account for these phenomena. They can be divided in two classes: (i) the models which are based entirely on statistical and geometrical grounds. The best known and most widely studied of them is the Random Sequential Adsorption (RSA) model which is discussed in details. For the processes in which gravity plays an important role one uses the Ballistic Deposition (BD) model. We also present models which are aimed at accounting for the behavior lying between the ballistic deposition and the RSA. (ii) The second type of models corresponds to those which take explicitly the diffusion of the particles in the vicinity of the adsorption plane into account. The results relative to these models, called diffusional models, are discussed in details. Finally, the last part of the review is devoted to experimental results. We show, in particular, that the Langmuir model, which is the most widely used model in the literature to account for the protein adsorption kinetics, does not predict correctly the experimental observations. We present and discuss in a critical way experimental evidence which seems to indicate the validity of the RSA and ballistic models.