The main goal of my research task was to examine various approaches to
space-time metrics that are commonly referred to as pp-waves and to unify
the notation and definitions of these objects. In my talk I shall present
the audience with some of the definitions and especially highlight the
relationships between these various approaches. After settling what the term
pp-wave consists of, and what the heuristics for introducing such object
are, I shall introduce some of the basic properties, as well as some of the
more advanced classical results (Brinkmann and Rosen coordinates transition,
Penrose limit).