Around 2000, Morel and Voevodsky developed a homotopy theory for algebraic varieties that uses 𝔸^1 as an interval. Via Steenrod operations for motivic cohomology, this theory played a fundamental role in the resolution of the Milnor and Block-Kato conjectures). However, 𝔸^1 is not contractible in many interesting areas in mathematics, and in recent years, a number of enhancements of Morel—Voevodsky’s theory have been proposed. In this talk we compare two of them: one built for log schemes, and one built for modulus pairs (or marked schemes in D'Addezio’s terminology).