European shoe sizes are based on the Paris Point system (1 size = 6.67mm), while US sizes use a different 1/3-inch increment. The conversion isn't perfectly linear, but reliable rules of thumb exist.
Women: subtract about 31 from the EU size to get US. EU 37 ≈ US 6.5, EU 38 ≈ US 7.5, EU 39 ≈ US 8.5, EU 40 ≈ US 9.
Men: subtract about 33. EU 41 ≈ US 8, EU 42 ≈ US 8.5, EU 43 ≈ US 9.5, EU 44 ≈ US 10, EU 45 ≈ US 11.
When in doubt, measure your foot in centimeters from heel to longest toe. Most brands publish a foot-length-to-size chart that's more accurate than label conversion.
Italian luxury brands (Gucci, Prada) often run a half-size small. Order one half-size up if buying online.