Giant-amplitude oscillations in dc magnetoresistance of a high-mobility two-dimensional electron system can be induced by millimeterwave irradiations, leading to zero-resistance states at the oscillation minima. Following a brief overview of the now well-known phenomenon, this paper reports on aspects of more recent experiments on the subject. These are: new zero-resistance states associated with multi-photon processes; suppression of Shubnikov-de Haas oscillations by high-frequency microwaves; and microwave photoconductivity of a high-mobility two-dimensional hole system.