  Main results and techniques of the fractional calculus of variations are
surveyed. We consider variational problems containing Caputo derivatives and
study them using both indirect and direct methods. In particular, we provide
necessary optimality conditions of Euler-Lagrange type for the fundamental,
higher-order, and isoperimetric problems, and compute approximated solutions
based on truncated Gr\"{u}nwald--Letnikov approximations of Caputo derivatives.
