This colloquium will give a brief introduction to reservoir computing, an overview of its theoretical foundations, including the notion of a universal family of reservoir computers that is capable of approximating a certain family of nonlinear maps from input sequences to output sequences, as well as its inherent limitations. It will then motivate and touch on efforts by the speaker and his collaborators to exploit noisy near-term quantum computers as quantum reservoir computers. Finally, the colloquium will conclude with a discussion of research directions for further development of quantum reservoir computers as well as research trends in the broader recent efforts on engineered physical learning machines going beyond reservoir computers.