In recent years, variants of the two-level Schwarz algorithm have been developed in collaboration between Clark Dohrmann of Sandia-Albuquerque and a group at the Courant Institute. By a modification of the coarse component of the preconditioner, borrowed in part from older domain decomposition methods of iterative substructuring type, the new methods are easier to implement for general subdomain geometries and can be made insensitive to large variations on the coefficients of the partial differential equation across the interface between the subdomains. After an introduction to the design of these methods, results on applications to almost incompressible elasticity and Reissner-Mindlin plates - solved by using mixed finite elements - and problems posed in H(div) and H(curl) will be discussed. Some of these results will appear in the doctoral dissertations of Jong Ho Lee and Duk-soon Oh, two PhD candidates at the Courant Institute.