Toury (1995, 2012) distinguishes between cognitive translation acts on the one hand, and sociological translation events on the other; a translation act is embedded in a translation event, and both acts and events are seen as processes. He also explains three senses of ‘translation problem,’ which relate to different notions of the processes involved in the translation act. The present paper analyses and develops these ideas. It distinguishes between what are here labeled virtual, reverse-engineered, and actual processes of translation acts or events, which correlate with Toury’s three senses of ‘translation problem.’ A few examples are given of models of each kind of process, both classical and more recent ones. Also discussed is the extent to which the various models are predictive and hence testable. To designate the translation process at the historical and cultural level, alongside the mental act and the situational event, the term ‘translation practice’ is suggested.