This chapter deals with free-boundary problems for liquid crystals. It presents several papers, which deal with the equilibrium shapes of a drop of liquid crystal surrounded by an isotropic fluid. The prototype of this problem was first considered by Oseen. The chapter considers drops of nematic liquid crystals surrounded by isotropic fluids. It provides an approximate solution to a fascinating problem, namely to the problem of finding the stable equilibrium shape of a drop free to float on a dense substrate. It discusses two limiting problems which are slightly easier to solve than the general equilibrium problem. The chapter also looks at the equilibrium shapes of a drop among some special regular regions: those whose boundary possesses at most one edge. There is indeed enough evidence that for many nematic liquid crystals the homeotropic boundary condition holds at the interface with air.