  We review some important ideas in the design and analysis of robust
overlapping domain decomposition algorithms for high-contrast multiscale
problems and propose a domain decomposition method better performance in terms
of the number of iterations. The main novelty of our approaches is the
construction of coarse spaces, which are computed using spectral information of
local bilinear forms. We present several approaches to incorporate the spectral
information into the coarse problem in order to obtain minimal coarse space
dimension. We show that using these coarse spaces, we can obtain a domain
decomposition preconditioner with the condition number independent of contrast
and small scales. To minimize further the number of iterations until
convergence, we use this minimal dimensional coarse spaces in a construction
combining them with large overlap local problems that take advantage of the
possibility of localizing global fields orthogonal to the coarse space. We
obtain a condition number close to 1 for the new method. We discuss possible
drawbacks and further extensions.
