Let $X$ be a symmetric space of noncompact type, and let $\Gamma$ be a lattice in the isometry group of $X$. We study the distribution of orbits of $\Gamma$ acting on the symmetric space $X$ and its geometric boundary $X(\infty )$, generalizing the main equidistribution result of Margulis's thesis [M, Theorem 6] to higher-rank symmetric spaces. More precisely, for any $y\in X$ and $b\in X(\infty )$, we investigate the distribution of the set $\{(y\gamma ,b{\gamma }^{-1}):\gamma \in \Gamma \}$ in $X\times X(\infty )$. It is proved, in particular, that the orbits of $\Gamma$ in the Furstenberg boundary are equidistributed and that the orbits of $\Gamma$ in $X$ are equidistributed in “sectors” defined with respect to a Cartan decomposition. Our main tools are the strong wavefront lemma and the equidistribution of solvable flows on homogeneous spaces, which we obtain using Shah's result [S, Corollary 1.2] based on Ratner's measure-classification theorem [R1, Theorem 1]