Intuitively, science progresses from truth to truth. A glance at history quickly reveals that this idea is mistaken. We often learn from scientific theories that turned out to be false. This chapter focuses on a different challenge: idealisations are deliberately and ubiquitously used in science. Scientists thus work with assumptions that are known to be false. Any account of scientific progress needs to account for this widely accepted scientific practice. It is examined how the four dominant accounts – the problem-solving account, the truthlikeness account, the epistemic account, and the noetic account – can cope with the challenge from idealisation, with an eye on indispensable idealisations. One upshot is that, on all accounts, idealisations can promote progress. Only some accounts allow them to constitute progress.