Abstract: A result by Ozsvath and Szabo states that the knot Floer complex of an L-space knot is a staircase. In this talk, we will discuss a similar result for two-component L-space links: the link Floer complex of such links can be thought of as an array of staircases. We will describe an algorithm to extract this array directly from the H-function of the link. As an application, we will discuss how to use this and the link surgery formula to compute the knot Floer complex and the tau-invariant of a certain class of satellite knots. Using that, we partially confirm a conjecture of Hedden and Pinzon-Caicedo: If P is an L-space satellite operator which acts as a group homomorphism on the smooth concordance group, then P is either the zero operator, the identity operator, or the orientation reversing operator. This is joint work with Ian Zemke .