Active matter theories generally augment descriptions of passive liquid crystals with nonequilibrium forces and currents, thereby addressing how activity affects these structures. In this talk, I will ask a less common question: can activity create new liquid crystals -- spatiotemporal structures impossible in passive systems? I will demonstrate that the interplay of chiral asymmetry, which is important in multiple experimental situations, and activity yields new liquid crystalline phases. I will describe two such states -- a time-cholesteric phase and a time-crystalline phase with hexatic spatial correlations -- in detail, both of which may have already been observed in experiments. Further, unlike in equilibrium, where chirality must be structural, non-reciprocal interactions in active systems can lead to the formation of these new liquid-crystalline phases even when the elementary units have no chiral asymmetry. Together, my talk will explore new liquid crystalline organisations allowed in active systems, describe their properties and finally suggest how they may be synthesised.