The goal of this talk is to introduce the notion of lax idempotent monads, or more generally, lax idempotent algebras, in the context of homotopy-coherent mathematics. After reviewing the main definitions and properties, I will give examples of lax idempotent monads appearing in the theory of fibrations of (?,1)-categories, (co)completions, and (?,1)-operads. This is joint work with Thomas Blom.