Revue article, 8 pages, 6 figures ; Vacuum field fluctuations exert radiation pressure on mirrors in quantum vacuum. For a pair of mirrors this effect is well known as the Casimir effect. When a single mirror is moving in vacuum, radiation pressure leads to a dissipative force which opposes itself to the mirrors motion. Accordingly the electromagnetic field does not remain in the vacuum state but photons are emitted by the mirror into vacuum. This paper describes the photon emission of a high-finesse cavity oscillating globally in quantum vacuum. Common features and differences with usual parametric processes in quantum optics are discussed. Interesting signatures of quantum radiation like pulse shaping and frequency up-conversion are predicted, which could be used to experimentally demonstrate motion-induced dissipative effects. The feasibility of an experimental realization is discussed in the end of the paper.