A topic of considerable current interest in applied mathematics is wavelets. The promises of wavelets are based upon their localization in both spatial and spectral domains, better convergence properties, their computational speed, and the two parameter invariance under analytic representations. Recently Wavelets have been used in signal processing and computer vision with great success. In electromagnetics (EM), orthonormal wavelets have been applied to the method of moments as basis and testing functions in the integral equations to replace the pulse, triangle, and PWS (piecewise sinusoidal) functions. Very sparse coefficient matrices have been obtained due to the vanishing moments, localization, and MRA (multiresolution analysis) of the wavelets. In the modeling of microwave active devices, the interpolating wavelets (IWL) were employed to solve nonlinear equations with great success. In this paper we introduce the basic wavelet theory, summarize the wavelet properties and present the applications of wavelets to the lossy and dispersive transmission lines, EM wave scattering and semiconductor modeling problems.