In this series of lectures we review three works on the decay of generalized almost periodic solutions of viscous and non-viscous conservations laws. Namely, we start by reviewing a paper by Frid (2002), which first establishes a general framework to study the decay of Stepanoff-Wiener almost periodic solutions for systems of viscous and non-viscous conservation laws and its applications to many different types of systems, both viscous and non-viscous, including the case of a scalar conservation law in several space variables. The second work we review is a recent paper by E.~Panov (2016) which establishes the decay of Besicovitch almost periodic solutions of scalar conservation laws in several space variables,
which extends the corresponding result contained in Frid (2002). Finally, we review the a recent result by Frid (2017) which
establishes the decay of Besicovitch almost periodic solutions for certain degenerate anisotropic parabolic-hyperbolic equations, under restrictions on the initial data.