  We survey our recent results on stability of 3D crystals in the
Schr\"odinger-Poisson-Newton model. We establish orbital stability for the
ground state in the case of finite crystal and linear stability for infinite
crystals under novel Jellium and Wiener conditions on the charge density of
ions. The corresponding examples are given. In the case of finite crystals, the
proofs rely on positivity of the Hessian of Hamiltonian functional in the
directions orthogonal to the manifold of ground states. The problem of spatial
periodicity of the ground states is discussed. The non-periodic examples are
constructed. In the case of infinite crystals the proofs rely on a novel
spectral theory of Hamiltonian operators which is a special version of the
Gohberg-Krein-Langer theory of selfadjoint operators in the Hilbert spaces with
indefinite metric. We establish the existence of the ground states and the
dispersive decay for the linearised dynamics.
