Archaea are abundant in marine and terrestrial aquatic environments, sediments, and soils. They inhabit at least an 85°C temperature range from the polar ocean to hydrothermal springs. Many Archaea produce membrane lipids called glycerol dialkyl glycerol tetraethers (GDGTs). Experiments on pure and enrichment cultures as well as an empirical correlation for marine sediments (the TEX86 index) together show positive relationships between temperature and the number of cyclopentane or cyclohexane rings in GDGTs. The resulting TEX86 paleotemperature proxy has been applied across a wide range of geologic history and depositional settings. The exact relationship between TEX86 and temperature, however, remains poorly understood. Environmental systems and cultures have different temperature dependencies, and the ecological niche(s) of aquatic Archaea are still a subject of active investigation. Here we review some of the remaining questions about GDGT paleotemperature proxies. Better answers to these challenging problems will help refine future paleoceanographic applications.