I study various finite geometrical substructures, mostly in projective spaces, many times in planes, like (multiple) blocking sets. Some substructures are also related to extremal graph theoretical questions, where the graph constructions arising from the finite geometrical substructures may provide interesting graph theoretical results, but also, the problems motivated by graph theoretical research may open new research areas in finite geometries. Multisets of finite projective spaces are aslo related to (error correcting) codes. Here finite geometrical substructures may also provide interesting constructions.