I will show that homotopy algebras "of a fixed type" form a category enriched over L-infinity algebras. I explain in what sense this enriched category stands behind the homotopy theory of homotopy algebras. This talk is based on papers: http://arxiv.org/abs/1406.1744 (joint with Chris Rogers) and http://arxiv.org/abs/1406.1751 (joint with Alex Hoffnung and Chris Rogers).