We introduce and discuss time-Floquet metamaterials, or artificial media possessing a double periodicity both in space and time. They can be obtained from a regular crystal by periodically modulating in time the physical properties of each unit cell, leading to a novel class of metamaterials where frequency is not conserved. By suitably breaking time-reversal symmetry, these classical systems can exhibit non-trivial topological properties that can be exploited to build novel, broadband nonreciprocal devices immune to defects and disorder both in their structure and in the modulation scheme. We discuss potential applications in acoustics and electromagnetism.