In high-Tc superconductors (HTSC) the thermal fluctuation of the vortex lattice (VL) may become large since the vortex lattice is soft due to the strong overlap of the vortex fields and since the temperature T can be high. It was thus argued that the three-dimensional (3D) vortex lattice is thermally entangled and may “melt”. This type of transition and the consequences of melting are not clear as yet since the always present pinning of the vortex cores by material inhomogeneities may cause similar disorder. In HTSC the pinning energy may become comparable with kBT because the coherence length ξ (vortex radius) is small and T may be high. Therefore, thermally activated depinning competes with possible effects of “flux melting”, and the “irreversibility line” in the B-T-plane (B=magnetic field) should better be called “depinning line”. Due to the diffusive character of flux motion the depinning line of a given experiment, a line of constant flux diffusivity D(T, B), depends on the frequency or sweep rate, on the size and shape of the superconductor, and on the field orientation; it is thus not a material property alone. In this review it is argued that theories predicting “new phases of vortex matter” (flux solid, flux liquid, vortex plasma, vortex glass, and hexatic vortex glass) may be improved by replacing the 2D straight-vortex interaction by the correct 3D interaction between all vortex segments. This interaction (a) facilitates vortex crossing and reconnection, (b) reduces the elastic energy of short-wavelength tilt by a very large factor (non-local elasticity), and (c) yields the correct reduction of the tilt energy by the crystal anisotropy. The non-local elasticity of the VL is reviewed and a general solution of the anisotropic London theory for arbitrary vortex arrangements is given. A very useful phenomenological theory of layered superconductors is the Lawrence-Doniach model, which defines a 2D Ginzburg-Landau function in each layer. The point vortices in the layers interact with each other magnetically and, between neighboring layers, by Josephson coupling. At sufficiently large fields their thermal fluctuation is quasi-2D and, at an in general different field, their pinning becomes 2D.