Quality measurement is a critical tool for improving palliative care and hospice, but significant research is needed to improve the application of quality indicators. We defined methodological priorities for advancing the science of quality measurement in this field based on discussions of the Technical Advisory Panel of the Measuring What Matters consensus project of the American Academy of Hospice and Palliative Medicine and Hospice and Palliative Nurses Association and a subsequent strategy meeting to better clarify research challenges, priorities, and quality measurement implementation strategies. In this article, we describe three key priorities: 1) defining the denominator(s) (or the population of interest) for palliative care quality indicators, 2) developing methods to measure quality from different data sources, and 3) conducting research to advance the development of patient/family-reported indicators. We then apply these concepts to the key quality domain of advance care planning and address relevance to implementation of indicators in improving care. Developing the science of quality measurement in these key areas of palliative care and hospice will facilitate improved quality measurement across all populations with serious illness and care for patients and families.