An overview of the current ongoing research about magnetic filaments performed at IFISC in collaboration with other scientific institutions will be presented. Magnetic filaments are akin to one dimensional magnetic polymers but at supra-molecular scale where magnetic nano-colloids are used as monomers. These filaments have a huge potential in industrial applications as enhanced substitutes of current ferrofluids, nano-actuators, or information storage applications, to mention just a few. The properties of these systems are by no means trivial, and numerical simulations play a key role to unveil the behaviour of filaments. In this talk we will first review the properties of single magnetic filaments placed in the bulk for both quiescent and flow conditions. In both cases we will address the zero and non-zero external magnetic field regimes. Then we will review the behaviour of magnetic brushes (sets of magnetic filaments grafted by one of their ends to a surface). In the latter case, tools associated to the analysis of networks have been found to be very helpful in order to determine the key properties of this complex systems.