One of the most important aspects of the scientific endeavour is the definition of specific concepts as precisely as possible. However, it is also important not to lose sight of two facts: (i) we divide the study of nature into manageable parts in order to better understand it owing to our limited cognitive capacities and (ii) definitions are inherently arbitrary and heavily influenced by cultural norms, language, the current political climate, and even personal preferences, among many other factors. As a consequence of these facts, clear-cut definitions, despite their evident importance, are oftentimes quite difficult to formulate. One of the most illustrative examples about the difficulty of articulating precise scientific definitions is trying to define the concept of a brain. Even though the current thinking about the brain is beginning to take into account a variety of organisms, a vertebrocentric bias still tends to dominate the scientific discourse about this concept. Here I will briefly explore the evolution of our 'thoughts about the brain', highlighting the difficulty of constructing a universally (or even a generally) accepted formal definition of it and using planarians as one of the earliest examples of organisms proposed to possess a 'traditional', vertebrate-style brain. I also suggest that the time is right to attempt to expand our view of what a brain is, going beyond exclusively structural and taxa-specific criteria. Thus, I propose a classification that could represent a starting point in an effort to expand our current definitions of the brain, hopefully to help initiate conversations leading to changes of perspective on how we think about this concept. This article is part of the theme issue 'Liquid brains, solid brains: How distributed cognitive architectures process information'.