  In this review, we present a derivation of the on-shell renormalization
conditions for scalar and fermionic fields in theories with and without parity
conservation. We also discuss the specifics of Majorana fermions. Our approach
only assumes a canonical form for the renormalized propagators and exploits the
fact that the inverse propagators are non-singular in $\varepsilon = p^2 -
m_n^2$, where $p$ is the external four-momentum and $m_n$ is a pole mass. In
this way, we obtain full agreement with commonly used on-shell conditions. We
also discuss how they are implemented in renormalization.
