  Given a group $G$ and an endomorphism $\varphi$ of $G$, two elements $x, y
\in G$ are said to be $\varphi$-conjugate if $x = gy \varphi(g)^{-1}$ for some
$g \in G$. The number of equivalence classes for this relation is the
Reidemeister number $R(\varphi)$ of $\varphi$. The set $\{R(\psi) \mid \psi \in
\mathrm{Aut}(G)\}$ is called the Reidemeister spectrum of $G$. We investigate
Reidemeister numbers and spectra on direct products of finitely many groups and
determine what information can be derived from the individual factors.
