Cells have the amazing ability of reshaping themselves to perform different functions, from division to motion. In order to do that, they exploit active forces exerted by the cytoskeleton, a set of active filaments with partnered molecular motors that not only provide a structural scaffold to the cell but can also dynamically self-organize in order to exert the right forces at the right time. However, how exactly the microscopic interaction between filaments and motors can lead to specific organizations of the cytoskeleton is unclear. To shed light on these issues, we reconstitute minimal experimental systems based on purified cytoskeletal proteins and investigate their ability to self-organize. Specifically, by using an experimental setup in which cytoskeletal filaments propelled by molecular motors actively glide on a surface, we show how different microscopic interactions between filaments lead to diverse macroscopic patterns. We then use this system to investigate how patterns are shaped by changing the topology of the system (from planar to spherical) and by the introduction of defects in the alignment of filaments (nematic defects). Our results shed light on the self-organization properties of the cytoskeleton but also indicate strategies to control pattern formation processes in general by playing with defects and with the topology of the system.