Abstract: Wavelet analysis is a refinement of Fourier analysis. There are a lot of applications of wavelet analysis in signal and image processing besides many other fields of vital importance. In the recent years several refinements of wavelets have been studied and it has been demonstrated that their performance or performance of wavelets coupled with other methodologies such as ANFIS and Fuzzy out performs wavelet methods. Inverse problems are often encountered in different areas of science and engineering. Wavelet analysis play very significant role in solving inverse problems modeling real world problems. In this talk a brief review of these developments including the current work of the research group of the speaker will be discussed.