The United Nations Framework Convention on Climate Change (UNFCCC) process agreed in Paris to limit global surface temperature rise to “well below 2°C above pre-industrial levels.” But what period is preindustrial? Somewhat remarkably, this is not defined within the UNFCCC’s many agreements and protocols. Nor is it defined in the IPCC’s Fifth Assessment Report (AR5) in the evaluation of when particular temperature levels might be reached because no robust definition of the period exists. Here we discuss the important factors to consider when defining a preindustrial period, based on estimates of historical radiative forcings and the availability of climate observations. There is no perfect period, but we suggest that 1720–1800 is the most suitable choice when discussing global temperature limits. We then estimate the change in global average temperature since preindustrial using a range of approaches based on observations, radiative forcings, global climate model simulations, and proxy evidence. Our assessment is that this preindustrial period was likely 0.55°–0.80°C cooler than 1986–2005 and that 2015 was likely the first year in which global average temperature was more than 1°C above preindustrial levels. We provide some recommendations for how this assessment might be improved in the future and suggest that reframing temperature limits with a modern baseline would be inherently less uncertain and more policy relevant.