The purpose of the talk is to explain the problem of isometric embeddability à la Nash for Lorentzian manifolds. This includes: (a) Simple ways to reduce the problem of embeddability to the (positive definite) Riemannian case, when a semi-Euclidean space of arbitrary signature is allowed as embedding space. (b) A sharp characterization of the class of Lorentzian manifolds isometrically embeddable when the embedding space is Lorentz-Minkowski one. (c) To sketch a proof that globally hyperbolic spacetimes (i.e., the most important class of Lorentzian manifolds in Mathematical Relativity) belong to this class. With this aim, some flavour of the Lorentzian tools and related problems of splitting of spacetimes will be given. The talk is based in joint work with Olaf Müller (Trans. Amer. Math. Soc. 363, 2011).