Breathing in mammals is a seemingly straightforward behaviour controlled by the brain. A brainstem nucleus called the preBötzinger Complex sits at the core of the neural circuit generating respiratory rhythm. Despite the discovery of this microcircuit almost 25 years ago, the mechanisms controlling breathing remain elusive. Given the apparent simplicity and well-defined nature of regulatory breathing behaviour, the identification of much of the circuitry, and the ability to study breathing in vitro as well as in vivo, many neuroscientists and physiologists are surprised that respiratory rhythm generation is still not well understood. Our view is that conventional rhythmogenic mechanisms involving pacemakers, inhibition or bursting are problematic and that simplifying assumptions commonly made for many vertebrate neural circuits ignore consequential detail. We propose that novel emergent mechanisms govern the generation of respiratory rhythm. That a mammalian function as basic as rhythm generation arises from complex and dynamic molecular, synaptic and neuronal interactions within a diverse neural microcircuit highlights the challenges in understanding neural control of mammalian behaviours, many (considerably) more elaborate than breathing. We suggest that the neural circuit controlling breathing is inimitably tractable and may inspire general strategies for elucidating other neural microcircuits.