Modeling the mycelium morphology of filamentous fungi is valuable in connection with studies of their growth mechanisms, i.e. tip extension and branching, and in this work a general frame for morphological models is presented. The general frame consist of a population balance equation (PBE) for a two-dimensional density function, which describes the properties, i.e. the number of tips and the total hyphal length, of a population of hyphal elements. From the general PBE, balances for the average properties of the population can be derived. After presentation of the general model frame the kinetics for the different processes influencing the mycelium morphology, i.e. spore germination, growth, and hyphal fragmentation, are reviewed. Thereafter follows an overview of different kinetic models presented in the literature. The models are divided into four groups: single hyphal element/branch models; average property models; population models; and morphological structured models. Models within the first three groups are discussed and presented within the general frame. Finally some solutions to the general PBE are presented and aspects on model verification based on experimental data are discussed.