We provide a survey of recent results on pseudo-parallel spacelike and timelike surfaces, including the relationship between the properties of pseudoparallelism and \(\lambda \) -isotropy, their classification in low codimension, and their existence by giving many interesting examples. Moreover, we obtain a nonexistence result of pseudo-parallel spacelike surfaces with non-flat normal bundle in a class of semi-Riemannian warped products of dimension 4.