  Herein we survey the main results concerning quantum automata and machines
with classical control. These machines were originally proposed by Sernadas et
al in [37], during the FCT QuantLog project. First, we focus on the
expressivity of quantum automata with both quantum and classical states. We
revise the result obtained in [32] where it was proved that such automata are
able to recognise, with exponentially less states than deterministic finite
automata, a family of regular languages that cannot be recognised by other
types of quantum automata. Finally, we revise the concept of quantum Turing
machine with classical control introduced in [25]. The novelty of these
machines consists in the fact that their termination problem is completely
deterministic, in opposition to other notions in the literature. Concretely, we
revisit the result that such machines fulfil the s-m-n property, while keeping
the expressivity of a quantum model for computation.
