Let G be a reductive group, T be a torus and Ψ be a root datum associated with T. In this talk, I will discuss when we can embed T to G as a maximal torus with respect to the root datum Ψ. Over local fields, the existence of such embedding is determined by the Tits indices of G and Ψ. Then I will use this to construct an example where the local-global principle for the embedding fails. I will also explain the relation between the embeddings of root data into reductive groups and embeddings of étale algebras with involution into central simple algebras with involution. The latter was discussed in G. Prasad and A. Rapinchuk's paper.