Aesthetic values feature prominently in science and shape what theories and experiments are pursued, what explanations are considered satisfactory, and whether theories are trusted. What significance should such values be given and should they impact our attitudes towards scientific products? This chapter explores these questions and how throughout scientific progress the questions we ask about the role of aesthetic values might change. We start with the traditional distinction between context of discovery and context of justification and show that neither context is value-proof. Then we illustrate how aesthetic values shape different levels of scientific activities, from designing experiments and reconstructing fossils, to evaluating data. We then explore how we could justify the epistemic import of aesthetic values and develop some concerns. Last, the chapter asks whether we should expect the questions surrounding aesthetic values in scientific practice to change with scientific progress, as we enter the era of post-empirical physics, big data science, and make more discoveries using machine learning and artificial intelligence (AI).