  We obtain a formula for the Heegaard Floer homology (hat theory) of the
three-manifold $Y(K_1,K_2)$ obtained by splicing the complements of the knots
$K_i\subset Y_i$, $i=1,2$, in terms of the knot Floer homology of $K_1$ and
$K_2$. We also present a few applications. If $h_n^i$ denotes the rank of the
Heegaard Floer group $\widehat{\mathrm{HFK}}$ for the knot obtained by
$n$-surgery over $K_i$ we show that the rank of
$\widehat{\mathrm{HF}}(Y(K_1,K_2))$ is bounded below by
$$\big|(h_\infty^1-h_1^1)(h_\infty^2-h_1^2)- (h_0^1-h_1^1)(h_0^2-h_1^2)\big|.$$
We also show that if splicing the complement of a knot $K\subset Y$ with the
trefoil complements gives a homology sphere $L$-space then $K$ is trivial and
$Y$ is a homology sphere $L$-space.
