  When looking for analytical approaches to treat frustrated quantum magnets,
it is often very useful to start from a limit where the ground state is highly
degenerate. This chapter discusses several ways of deriving {effective
Hamiltonians} around such limits, starting from standard {degenerate
perturbation theory} and proceeding to modern approaches more appropriate for
the derivation of high-order effective Hamiltonians, such as the perturbative
continuous unitary transformations or contractor renormalization. In the course
of this exposition, a number of examples taken from the recent literature are
discussed, including frustrated ladders and other dimer-based Heisenberg models
in a field, as well as the mapping between frustrated Ising models in a
transverse field and quantum dimer models.
