  Molecular communication (MC) is a new communication engineering paradigm
where molecules are employed as information carriers. MC systems are expected
to enable new revolutionary applications such as sensing of target substances
in biotechnology, smart drug delivery in medicine, and monitoring of oil
pipelines or chemical reactors in industrial settings. As for any other kind of
communication, simple yet sufficiently accurate channel models are needed for
the design, analysis, and efficient operation of MC systems. In this paper, we
provide a tutorial review on mathematical channel modeling for diffusive MC
systems. The considered end-to-end MC channel models incorporate the effects of
the release mechanism, the MC environment, and the reception mechanism on the
observed information molecules. Thereby, the various existing models for the
different components of an MC system are presented under a common framework and
the underlying biological, chemical, and physical phenomena are discussed.
Deterministic models characterizing the expected number of molecules observed
at the receiver and statistical models characterizing the actual number of
observed molecules are developed. In addition, we provide channel models for
time-varying MC systems with moving transmitters and receivers, which are
relevant for advanced applications such as smart drug delivery with mobile
nanomachines. For complex scenarios, where simple MC channel models cannot be
obtained from first principles, we investigate simulation-driven and
experimentally-driven channel models. Finally, we provide a detailed discussion
of potential challenges, open research problems, and future directions in
channel modeling for diffusive MC systems.
