Two sets of signature and normalization conventions are in use for NP formalism: formula_12 and formula_13. The former is the original one that was adopted when NP formalism was developed and has been widely used in black-hole physics, gravitational waves and various other areas in general relativity. However, it is the latter convention that is usually employed in contemporary study of black holes from quasilocal perspectives (such as isolated horizons and dynamical horizons). In this article, we will utilize formula_13 for a systematic review of the NP formalism (see also refs.).