I will discuss the concept of rearrangement-invariant function spaces and provide a brief outline of my own work related to this topic. In particular, recent results of my collaboration with Z. Mihula (FEE CTU Prague, member of CAAS) and J. Soria (UC Madrid) will be presented. These involve a description of rearrangement-invariant hulls of weighted Lebesgue spaces as well as related inequalities concerning various types of rearrangements.