We explore the topology of real Lagrangian submanifolds in symplectic manifolds towards their uniqueness and classification. We prove that a real Lagrangian in a closed symplectic manifold is unique up to smooth cobordism. We then discuss the classification of real Lagrangians in $$extract_itex$$CP^2$$/extract_itex$$ and $$extract_itex$$S^2times S^2$$/extract_itex$$. Finally, we explain why it is tempting to conjecture that any real Lagrangian torus in $$extract_itex$$S^2times S^2$$/extract_itex$$ is Hamiltonian isotopic to the Clifford torus.