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Abstract The loss of life and economic consequences caused by several recent earthquakes demonstrate the importance of developing seismically safe building codes. The quantification of seismic hazard, which describes the likelihood of earthquake‐induced ground shaking at a site for a specific time period, is a key component of a building code, as it helps ensure that structures are designed to withstand the ground shaking caused by a potential earthquake. Geologic or geomorphic data represent important inputs to the most common seismic hazard model (probabilistic seismic hazard analyses, or PSHAs), as they can characterize the magnitudes, locations, and types of earthquakes that occur over long intervals (thousands of years). However, several recent earthquakes and a growing body of work challenge many of our previous assumptions about the characteristics of active faults and their rupture behavior, and these complexities can be challenging to accurately represent in PSHA. Here, we discuss several of the outstanding challenges surrounding geologic and geomorphic data sets frequently used in PSHA. The topics we discuss include how to utilize paleoseismic records in fault slip rate estimates, understanding and modeling earthquake recurrence and fault complexity, the development and use of fault‐scaling relationships, and characterizing enigmatic faults using topography. Making headway in these areas will likely require advancements in our understanding of the fundamental science behind processes such as fault triggering, complex rupture, earthquake clustering, and fault scaling. Progress in these topics will be important if we wish to accurately capture earthquake behavior in a variety of settings using PSHA in the future.