Computational Methods for Applied InverseProblems covers many directions in the moderntheory of inverse and illposed problems: mathematical physics, optimal inverse design, inverse scattering, inverse vibration, biomedical imaging, oceanography, seismic imaging and remote sensing; methods including standard regularization, parallel computing for multidimensional problems, Nystr#m method, numerical differentiation, analytic continuation, perturbationregularization, filtering, optimization and sparse solving methods are fully addressed. This issue attempts to bridge the gap between theoretical studies of ill-posed inverse problemsand practical applications.