The scientific study of animal minds is difficult. This book examines the most significant reasons this is so: seven challenges for the science to overcome. Researchers are aware of these challenges, but few take any of them head-on, and none address them collectively. Despite this focus on challenges, the book's attitude is optimistic rather than critical; these are challenges for the science, not challenges to the science. Researchers have made substantial progress as things are. But taking the challenges head-on can help build an even stronger, more vibrant science. The seven challenges are: 1) underdetermination of theory by data, 2) anthropomorphic bias, 3) the difficulty of modeling cognitive processes, 4) integrating across disciplines, 5) ecological validity, 6) small sample sizes, and 7) measuring consciousness. For each, the book suggests rethinking the challenge and reorienting our attempts to address it. These approaches are novel, general ways of thinking that will help researchers work through the challenges, and perhaps find solutions appropriate to their own research. Each of the main chapters takes on one challenge. Each also includes an empirical case study, from social reasoning in chimpanzees, to foraging in honeybees, to consciousness in octopuses. Along the way, a big-picture framework emerges for drawing conclusions about animal minds based on experimental evidence. In this framework, the role of any individual piece of the science is limited: any individual experiment, model, claim, or argument can only tell us so much. When we are appropriately modest about each piece, conclusions about animal minds must be arrived at by holistically considering all the evidence we can get. This is a work in the philosophy of science, but it is written to be accessible to any philosopher interested in empirical issues relating to the mind, researchers in any of the related sciences, including psychology, neuroscience, ethology, and evolutionary biology, as well as intermediate to advanced students.