The M/M/∞ queue can be considered as a compartmental system which may be modified by allowing its arrival and service rates to depend on an exogenous ‘environment process’. The states of the environment process are known as environments. We present some examples of this, chosen for their analytic or algorithmic tractability. We discuss (i) models with arrivals in only one environment, (ii) models with service in only one environment, (iii) reversible models and (iv) a model in which the environment process is also a queue.