  The generalized Oberwolfach problem asks for a decomposition of a graph $G$
into specified 2-regular spanning subgraphs $F_1,\ldots, F_k$, called factors.
The classic Oberwolfach problem corresponds to the case when all of the factors
are pairwise isomorphic, and $G$ is the complete graph of odd order or the
complete graph of even order with the edges of a $1$-factor removed. When there
are two possible factor types, it is called the Hamilton-Waterloo problem.
  In this paper we present a survey of constructive methods which have allowed
recent progress in this area. Specifically, we consider blow-up type
constructions, particularly as applied to the case when each factor consists of
cycles of the same length. We consider the case when the factors are all
bipartite (and hence consist of even cycles) and a method for using circulant
graphs to find solutions. We also consider constructions which yield solutions
with well-behaved automorphisms.
