This chapter mostly concerns free-boundary problems for liquid crystals. The literature about them is so huge as to demand a whole book to describe it. Here, apart from the last section, I will mostly follow three papers, namely Virga (1989 and 1990) and Roccato and Virga (1990), 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 (1933). The list of further reading appended to this chapter attempts to indicate other problems akin to this, which have also received attention in recent times.