  We consider one-dimensional systems comprising either active run-and-tumble
particles (RTPs) or passive Brownian random walkers. These particles are either
noninteracting or have hardcore exclusions. We study the dynamics of a single
tracer particle embedded in such a system - this tracer may be either active or
passive, with hardcore exclusion from environmental particles. In an active
hardcore environment, both active and passive tracers show long-time
subdiffusion: displacements scale as $t^{1/4}$ with a density-dependent
prefactor that is independent of tracer type, and differs from the
corresponding result for passive-in-passive subdiffusion. In an environment of
noninteracting active particles, the passive-in-passive results are recovered
at low densities for both active and passive tracers, but transient caging
effects slow the tracer motion at higher densities, delaying the onset of any
$t^{1/4}$ regime. For an active tracer in a passive environment, we find more
complex outcomes, which depend on details of the dynamical discretization
scheme. We interpret these results by studying the density distribution of
environmental particles around the tracer. In particular, sticking of
environment particles to the tracer cause it to move more slowly in
noninteracting than in interacting active environments, while the anomalous
behaviour of the active-in-passive cases stems from a `snowplough' effect
whereby a large pile of diffusive environmental particles accumulates in front
of a RTP tracer during a ballistic run.
