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.⋆ This is the penultimate draft of an article that has been published in the edited volume New Philosophical Perspectives on Scientific Progress (Routledge), edited by Yafeng Shan. Please cite the published version: https://www.taylorfrancis.com/chapters/edit/10.4324/9781003165859-21/ scientific-progress-idealisation-insa-lawler1 Fleming saw that bacteria on an agar plate had been killed close to where a mould was accidentally growing. The analysis of this mould led to the discovery of penicillin. 2 They can be also distinguished from fictions (for details see Frigg and Hartmann, 2020, §2.2).3 Some omissions lead to a misrepresentation, e.g., models can omit so many aspects of their target phenomena that they do not qualify as accurate representations. 4 Norton focuses on idealised models. Idealisations are (or represent) "[...] a real or fictitious system, distinct from the target system [...]." (2012, 209) This is compatible with Jones' account. A gas model that assumes that gas molecules do not repel each other can be construed as a model of fictitious gases.