This study focused on “convolution integrals and their applications”. The study was designed to show the areas where convolution integrals are applicable and point out roles of convolution integrals in solving practical problems. The study found out that Laplace transforms, Fourier transforms and their inverses are basic concepts to deal convolution integrals. Also, the study found out that convolution integrals are used to find inverse Laplace transform of product of two transforms, and solve problems related to integral equations, non – homogeneous linear DEs, probability theory and linear, time – invariant (LTI) system.