The concept of stable space splittings has been introduced in the early 1990ies, as a convenient framework for
developing a unified theory of iterative methods for variational problems in Hilbert spaces, especially for solving
large-scale discretizations of elliptic problems in Sobolev spaces. The more recently introduced notions of frames
of subspaces and fusion frames turn out to be concrete instances of stable space splittings. However, driven
by applications to robust distributed signal processing, their study has focused so far on different aspects. The
paper surveys the existing results on stable space splittings and iterative methods, outlines the connection to
fusion frames, and discusses the investigation of quarkonial or multilevel partition-of-unity frames as an example
of current interest.