  An Eulerian walk (or Eulerian trail) is a walk (resp. trail) that visits
every edge of a graph $G$ at least (resp. exactly) once. This notion was first
discussed by Leonhard Euler while solving the famous Seven Bridges of
K\"{o}nigsberg problem in 1736. What if Euler had to take a bus? In a temporal
graph $(G,\lambda)$, with $\lambda: E(G)\to 2^{[\tau]}$, an edge $e\in E(G)$ is
available only at the times specified by $\lambda(e)\subseteq [\tau]$, in the
same way the connections of the public transportation network of a city or of
sightseeing tours are available only at scheduled times. In this scenario, even
though several translations of Eulerian trails and walks are possible in
temporal terms, only a very particular variation has been exploited in the
literature, specifically for infinite dynamic networks (Orlin, 1984). In this
paper, we deal with temporal walks, local trails, and trails, respectively
referring to edge traversal with no constraints, constrained to not repeating
the same edge in a single timestamp, and constrained to never repeating the
same edge throughout the entire traversal. We show that, if the edges are
always available, then deciding whether $(G,\lambda)$ has a temporal walk or
trail is polynomial, while deciding whether it has a local trail is NP-complete
even if it has lifetime~2. In contrast, in the general case, solving any of
these problems is NP-complete, even under very strict hypothesis.
