  In this paper we introduce multiplicative Dirac structures on Lie groupoids,
providing a unified framework to study both multiplicative Poisson bivectors
(i.e., Poisson group(oid)s) and multiplicative closed 2-forms (e.g., symplectic
groupoids). We prove that for every source simply connected Lie groupoid $G$
with Lie algebroid $AG$, there exists a one-to-one correspondence between
multiplicative Dirac structures on $G$ and Dirac structures on $AG$, which are
compatible with both the linear and algebroid structures of $AG$. We explain in
what sense this extends the integration of Lie bialgebroids to Poisson
groupoids carried out in \cite{MX2} and the integration of Dirac manifolds of
\cite{BCWZ}. We also explain the connection between multiplicative Dirac
structures and higher geometric structures such as $\mathcal{LA}$-groupoids and
$\mathcal{CA}$-groupoids.
