Mesoscale eddies are ubiquitous features of the global ocean circulation and play a key role in transporting ocean properties and modulating air–sea exchanges. Anticyclonic and cyclonic eddies are traditionally thought to be associated with anomalous warm and cold surface waters, respectively. Using satellite altimeter and microwave data, here we show that surface cold-core anticyclonic eddies (CAEs) and warm-core cyclonic eddies (WCEs) are surprisingly abundant in the global ocean—about 20% of the eddies inferred from altimeter data are CAEs and WCEs. Composite analysis using Argo float profiles reveals that the cold cores of CAEs and warm cores of WCEs are generally confined in the upper 50 m. Interestingly, CAEs and WCEs alter air–sea momentum and heat fluxes and modulate mixed layer depth and surface chlorophyll concentration in a way markedly different from the traditional warm-core anticyclonic and cold-core cyclonic eddies. Given their abundance, CAEs and WCEs need to be properly accounted for when assessing and parameterizing the role of ocean eddies in Earth’s climate system.