We study the existence and properties of travelling wave solutions of the Fisher-KPP reaction-diffusion-convection equation u_t + h(u)u_x = [D(u)u_x]_x + g(u), where the diffusivity D(u) is simply or doubly degenerate. Both the cases when D(0) and D(1) are possibly zero real values or infinity, are treated. We discuss the effects, due to the presence of a convective term, concerning the property of finite speed of propagation. Moreover, in the doubly degenerate case we show the appearance of new types of profiles and provide their classification according to sharp relations between the nonlinear terms of the model. An application is also presented, concerning the evolution of a bacterial colony.