<p>Heat waves/cold waves are among the pervasive extreme weather events, which affect ecosystem, natural resources, infrastructure, human health, and society. Although the heat wave/cold wave is commonly defined as a period of consecutive days when temperature is above/below a threshold, studies use different definitions of these events. This study uses different definitions and indicators to assess heat waves and cold spells in different regions that have been exposed to severe heat and cold waves in the past decades including Tehran, London, Madrid, New York, Shanghai, and Vancouver. Different features of the heat wave/cold spell including frequency, average temperature, intensity, and duration are evaluated for historical (1990–2000) and projection (2030–2040) period under three climate scenarios including SSP1-2.6, SSP2-4.5, and SSP5-8.5. Results show that, aligning with climate change, most features and indices of the projected heat waves and cold spells have an upward and downward trend in all case studies, respectively. In addition, this work develops a vulnerability (exposure) index called extreme wave index (EWI) to define a relative hazard and threat of these events in different regions. The developed index indicates that Tehran, London, and Madrid are expected to be at higher risk from heat waves, while Vancouver and Tehran are projected to be more vulnerable to cold wave threats. Results reveal that the severity of different features of the heat waves/cold waves varies based on different indicators and thresholds. This indicates the importance of using a proper set of definition and indicators based on the aim of the study. This comprehensive framework and analysis is valuable in developing adaptation and mitigation plans to reduce mortality and damages to different sectors like water-environment resources, agriculture, energy, health, and industry.</p>