AbstractModelling and forecasting crude oil price volatility is crucial in many financial and investment applications. The main purpose of this paper is to review and assess the current state of oil market volatility knowledge. It highlights the properties and characteristics of the oil price volatility that models seek to capture, and discuss the different modelling approaches to oil price volatility. Asymmetric response to price change, persistence and mean reversion, structural breaks, and possible market spillover of volatility are discussed. To complement the discussion, West Texas Intermediate futures price data are used to illustrate these properties using non‐parametric and conditional modelling methods. The generalised autoregressive conditional heteroskedasticity‐type models usually applied in the oil price volatility literature are also explored. We additionally examine the exogenous factors that may influence volatility in the oil markets.