While numerous studies have addressed changes in climate extremes, analyses of concurrence of climate extremes are scarce, and climate change effects on joint extremes are rarely considered. This study assesses the occurrence of joint (concurrent) monthly continental precipitation and temperature extremes in Climate Research Unit (CRU) and University of Delaware (UD) observations, and in 13 Coupled Model Intercomparison Project Phase 5 (CMIP5) global climate simulations. The joint occurrences of precipitation and temperature extremes simulated by CMIP5 climate models are compared with those derived from the CRU and UD observations for warm/wet, warm/dry, cold/wet, and cold/dry combinations of joint extremes. The number of occurrences of these four combinations during the second half of the 20th century (1951–2004) is assessed on a common global grid. CRU and UD observations show substantial increases in the occurrence of joint warm/dry and warm/wet combinations for the period 1978–2004 relative to 1951–1977. The results show that with respect to the sign of change in the concurrent extremes, the CMIP5 climate model simulations are in reasonable overall agreement with observations. However, the results reveal notable discrepancies between regional patterns and the magnitude of change in individual climate model simulations relative to the observations of precipitation and temperature.