Several chromatographic approaches have been established over the last decades for the production of pharmaceutically relevant viruses. Due to the large size of these products compared to other biopharmaceuticals, e.g., proteins, convective flow media have proven to be superior to bead-based resins in terms of process productivity and column capacity. One representative of such convective flow materials is membranes, which can be modified to suit the particular operating principle and are also suitable for economical single-use applications. Among the different membrane variants, affinity surfaces allow for the most selective separation of the target molecule from other components in the feed solution, especially from host cell-derived DNA and proteins. A successful membrane affinity chromatography, however, requires the identification and implementation of ligands, which can be applied economically while at the same time being stable during the process and non-toxic in the case of any leaching. This review summarizes the current evaluation of membrane-based affinity purifications for viruses and virus-like particles, including traditional resin and monolith approaches and the advantages of membrane applications. An overview of potential affinity ligands is given, as well as considerations of suitable affinity platform technologies, e.g., for different virus serotypes, including a description of processes using pseudo-affinity matrices, such as sulfated cellulose membrane adsorbers.