The development of a multicellular organism, such as a human or an animal, begins with the fertilization of an egg cell. Thereupon the organism grows by repeated cell divisions until the adult size is reached and growth stops. Although it is known that intrinsic mechanisms determine the final size of developing organs and organisms, the basic principles of growth control are still poorly understood. However, there is strong evidence that certain morphogens, which are a special class of signaling molecules, act as growth factors and play a key role in growth control. In this work, growth control is studied from a mainly theoretical viewpoint. A discrete vertex model describing the organization of cells by a network of polygons is used, including a description of the cell cycle and a description of dynamical morphogen distributions. Self-organized growth is studied by introducing growth rules that govern cell divisions based on the local morphogen level. This discrete description is complemented by a continuum theory to gain further insight into the dynamics of self-organized growth processes. The theoretical description is applied to the developing wing of the fruit fly Drosophila melanogaster. In the developing wing, which is an epithelium consisting of single-layered cell sheets, the morphogen Decapentaplegic (Dpp) acts as a key growth factor. Experimental data shows that the Dpp distribution is dynamic and adapts to the size of the developing wing. Two mechanisms that rely on a regulatory molecule species and lead to such a dynamic behaviour of the Dpp distribution are studied. Several growth rules are tested and the resulting growth behaviour is quantitatively compared to experimental data of the developing wing. A particular growth rule, that triggers a cell division when the local morphogen level has increased by a certain relative amount, is found to be consistent with experimental observations under normal and several perturbed conditions. It is shown that mechanical stresses that arise due to spatial growth inhomogeneities can have a stabilizing effect on the growth process.