Animal shelter research has seen significant increases in participation over the past several decades from academic organizations, private organizations, public entities, and even corporations that aims to improve shelter programs, processes, operations, and outcomes for the various stakeholders/participants involved in a shelter system (animals, humans, the community, wildlife, and the environment). These efforts are scattered through a huge variety of different research areas that are challenging to define and scope for organizations seeking to start new lines of research inquiry. This work aims to enumerate some of the most critical outstanding problems for research in animal sheltering in a conceptual framework that is intended to help direct research conversations toward the research topics of highest impact (with the highest quality outcomes possible). To this end, we define seven (7) key areas for research: animal behavior, adoptions and special needs populations, medical conditions, disease transmission, community, ecology, and wellness (one health), operations, and public-private-academic-corporate collaboration. Within each of these areas, we review specific problems and highlight examples of successes in each area in the past several decades. We close with a discussion of some of the topics that were not detailed in this manuscript but, nonetheless, deserve some mention. Through this enumeration, we hope to spur conversation around innovative methodologies, technologies, and concepts in both research and practice in animal sheltering.