  Based on a general transport theory for non-reciprocal non-Hermitian systems
and a topological model that encompasses a wide range of previously studied
models, we (i) provide conditions for effects such as reflectionless and
transparent transport, lasing, and coherent perfect absorption, (ii) identify
which effects are compatible and linked with each other, and (iii) determine by
which levers they can be tuned independently. For instance, the directed
amplification inherent in the non-Hermitian skin effect does not enter the
spectral conditions for reflectionless transport, lasing, or coherent perfect
absorption, but allows to adjust the transparency of the system. In addition,
in the topological model the conditions for reflectionless transport depend on
the topological phase, but those for coherent perfect absorption do not. This
then allows us to establish a number of distinct transport signatures of
non-Hermitian, nonreciprocal, and topological behaviour, in particular (I)
reflectionless transport in a direction that depends on the topological phase,
(II) invisibility coinciding with the skin-effect phase transition of
topological edge states, and (III) coherent perfect absorption in a system that
is transparent when probed from one side.
