An asymmetric space is a set endowed with a distance that does not satisfy the axiom of symmetry. The asymmetric distance induces two topologies τ + and τ −, called the forward and backward topologies, respectively, which provide two versions for some notions, such as convergence, completeness, and compactness, and others. Some fixed point results of classical theory, such as Banach’s Fixed Point Theorem, have been extended to asymmetric spaces. In this work, we will extend to asymmetric spaces some fixed point results for contractions, contractive maps and non-expansive maps.