Nowadays inverse problems and applications in science and engineering represent an extremely active research field. The subjects are related to mathematics physics geophysics geochemistry oceanography geography and remote sensing astronomy biomedicine and other areas of applications. This monograph reports recent advances of inversion theory and recent developments with practical applications in frontiers of sciences especially inverse design and novel computational methods for inverse problems. The practical applications include inverse scattering chemistry molecular spectra data processing quantitative remote sensing inversion seismic imaging oceanography and astronomical imaging. The book serves as a reference book and readers who do research in applied mathematics engineering geophysics biomedicine image processing remote sensing and environmental science will benefit from the contents since the book incorporates a background of using statistical and non-statistical methods e.g. regularization and optimization techniques for solving practical inverse problems.