Time-space crystalline structures merge the ideas of time and space crystals to form a system that is periodic both temporally and spatially. The spatial part of the crystalline structure is created by an optical lattice and the temporal periodicity is engineered by choosing a proper resonant periodic driving of the spatial part. In the one-dimensional case, each site of the driven lattice comes equipped with a periodic temporal structure arising from the periodically oscillating localized wavepackets. Such a procedure creates a two-dimensional time-space crystalline structure. Extending the system to three spatial dimensions realizes a six-dimensional time-space crystalline structure which allows to probe high-dimensional condensed matter physics.