Recently, there has been a surge of interest for object-centric learning in neural network research. To many researchers, it seems clear that objects hold great potential for enabling more systematic generalisation, building compositional models of the world, and as grounding for language and symbolic reasoning. However, despite strong intuitions, a general definition of what constitutes an object is still lacking, and the precise notion of objects remains largely elusive. In this talk I aim to challenge some common intuitive conceptions about objects, and point to some of their subtle complexity. After that, I will present a few relevant findings from cognitive psychology regarding human object perception, and conclude by discussing a few challenges and promising approaches for incorporating objects into neural networks.