Obesity is now considered a chronic relapsing progressive disease, associated with increased all-cause mortality that scales with body weight, affecting more than 1 billion people worldwide. Excess body fat is strongly associated with excess energy intake, and most successful anti-obesity medications (AOMs) counter this positive energy balance through the suppression of eating to drive weight loss. Historically, AOMs have been characterized by modest weight loss and side effects which are compliance-limiting, and in some cases life-threatening. However, the field of obesity pharmacotherapy has now entered a new era of AOMs based on analogues of the gut hormone and neuropeptide glucagon-like peptide-1 (GLP-1). The latest versions of these drugs elicit unprecedented levels of weight loss in clinical trials, which are now starting to be substantiated in real-world usage. Notably, these drugs reduce weight primarily by reducing energy intake, via activation of the GLP-1 receptor on multiple sites of action primarily in the central nervous system, although the most relevant sites of action, and the neural circuits recruited remain contentious. Here we provide a targeted synthesis of recent developments in the field of GLP-1 neurobiology, highlighting studies which have advanced our understanding of how GLP-1 signaling modulates eating, and identify open questions and future challenges we believe still need to be addressed to aid the prevention and/or treatment of obesity.