  An $L$-space link is a link in $S^3$ on which all large surgeries are
$L$-spaces. In this paper, we initiate a general study of the definitions,
properties, and examples of $L$-space links. In particular, we find many
hyperbolic $L$-space links, including some chain links and two-bridge links;
from them, we obtain many hyperbolic $L$-spaces by integral surgeries,
including the Weeks manifold. We give bounds on the ranks of the link Floer
homology of $L$-space links and on the coefficients in the multi-variable
Alexander polynomials. We also describe the Floer homology of surgeries on any
$L$-space link using the link surgery formula of Ozsv\'{a}th and Manolescu. As
applications, we compute the graded Heegaard Floer homology of surgeries on
2-component $L$-space links in terms of only the Alexander polynomial and the
surgery framing, and give a fast algorithm to classify $L$-space surgeries
among them.
