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. Plain Language Summary Growing infrastructure and increasing population have caused significant loss of life due to recent large earthquakes, with the 2008 M w 7.9 Wenchuan and 2005 M w 7.6 Kashmir earthquakes each causing greater than 50,000 deaths. These earthquakes highlight the need for the development of building codes designed to withstand the strong ground shaking caused by earthquakes, as reinforced infrastructure is one of the most important factors for preventing fatalities due to ground shaking from earthquakes. Identifying the seismic hazard of a region, or the likelihood of ground shaking at a site due to potential earthquakes over time, is a key ingredient for informing a defensible building code. Here, we focus on current and future advances in how data from the fields of geology and geomorphology contribute to the most widely used type of seismic hazard model. These geologic data represent vital components to seismic hazard models, as they can provide information about the location and types of earthquakes that can occur over long, thousands of years, time periods, that cannot be obtained using other methods. We discuss some of the most pressing scientific issues about these data that are important for the development of seismic hazard models and defensible building codes.