The United Nations Framework Convention on Climate Change (UNFCCC) process agreed in Paris to limit global surface temperature rise to well below 2 degrees 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 ...