  The Hanani--Tutte theorem is a classical result proved for the first time in
the 1930s that characterizes planar graphs as graphs that admit a drawing in
the plane in which every pair of edges not sharing a vertex cross an even
number of times. We generalize this result to clustered graphs with two
disjoint clusters, and show that a straightforward extension to flat clustered
graphs with three or more disjoint clusters is not possible. For general
clustered graphs we show a variant of the Hanani--Tutte theorem in the case
when each cluster induces a connected subgraph. Di Battista and Frati proved
that clustered planarity of embedded clustered graphs whose every face is
incident with at most five vertices can be tested in polynomial time. We give a
new and short proof of this result, using the matroid intersection algorithm.
