It is estimated that ~60% of all stars (including brown dwarfs) have masses below 0.2Msun. Currently, there is no consensus on how these objects form. I will briefly review the four main theories for the formation of low-mass objects: turbulent fragmentation, ejection of protostellar embryos, disc fragmentation, and photo-erosion of prestellar cores. I will focus on the disc fragmentation theory and discuss how it addresses critical observational constraints, i.e. the low-mass initial mass function, the brown dwarf desert, and the binary statistics of low-mass stars and brown dwarfs. I will examine whether observations may be used to distinguish between different formation mechanisms, and give a few examples of systems that strongly favour a specific formation scenario. Finally, I will argue that it is likely that all mechanisms may play a role in low-mass star and brown dwarf formation.

6 pages, a short review, to appear in the proceedings of the conference "The labyrinth of star formation", edited by Stamatellos, Goodwin & Ward-Thompson