  We review results concerning homogeneous compacta and discuss some open
questions. It is established that indecomposable continua are Alexandroff
(resp., Mazurkiewicz, or strong Cantor) manifolds with respect to the class of
all continua. We also provide some new proofs of Bing's theorems about
separating metric compacta by hereditarily indecomposable compacta.
