This chapter provides a brief description of the numerical methods for solving linear and nonlinear integral equations, integro-differential equations and systems. Typically, these methods are based on the approximations like wavelets approximations, orthogonal polynomials and orthogonal functions approximations. In this chapter, we introduce the wavelet methods like Bspline wavelet method (BSWM), Legendre wavelet method (LWM), Legendre multi-wavelet method (LMWM), Chebyshev wavelet method (CWM), Haar wavelet method (HWM), Bernoulli wavelet method (BWM), polynomial approximation via Bernstein polynomials, Legendre spectral collocation method, Legendre polynomial, Block-Pulse functions, Sinc functions etc. which are applied to solve different types of integral equations.