The two-dimensional terpy embrace motif, a concert of multiple edge-to-face and offset-face-to-face interactions, assembles [M(terpy)₂]²⁺ complexes into regular square grids, as layers that are stacked in crystals. The layers possess deep segmented grooves on their surfaces, with the cavities occupied by small anions and sometimes by solvent. In this paper we survey and analyse the crystal packing in all known cases of this motif, together with new crystal structures and crystal growth information for [Ni(terpy)₂](PF₆)₂, [Ni(terpy)₂](PF₆)₂·acetone, and [Ni(terpy)₂](PF₆)₂·DMF. The main types of stacking patterns and interlayer domains are classified, in relation to absence or presence of solvation, and the resulting space-groups. The different structures of [Co(terpy)₂](ClO₄)₂·xH₂O, which can have strong influences on magnetic properties, are considered, and it is proposed that the subtle variations are due to a balance between optimal electrostatic stabilisation of the crystal when anions alone occupy the cavities, and hydrogen bonding (intra-layer and inter-layer) stabilisation when water is included. With larger anions and/or solvent molecules there is minor tilting of the M(terpy)₂ complexes such that the two surfaces of the layer are different. The patterns and principles of crystal packing for 2D M(terpy)₂ grids developed here are the foundation for subsequent descriptions and analyses of related crystal structures of derived compounds. The lack of published information about crystallisation conditions and processes is a limitation on the crystal engineering of these metal complex grids.