The notions of nonreciprocal properties in both photonics and materials have received significant traction recently, given their technological implications. Nonreciprocity can arise due to asymmetric property tensors, nonlinearity and spatio-temporal modulation. However, it can be enhanced in non-Hermitian as well as topological settings. For instance, many important properties of materials such as the optical diode effect depend on the interplay between the concepts of reciprocity, chirality and broken spatial and temporal symmetries. I will illustrate these concepts through a number of examples including nonreciprocal directional dichroism. Specifically, I will discuss the conditions for nonreciprocity of ferro-rotational order in several materials and indicate the use of linear optical gyration and possibly vortex beams as a likely way to detect ferro-rotational domains. The concept of vector order parameters will be then generalized to second- and higher-rank tensor order parameters. Finally, I will elucidate how to achieve hightemperature optical diode effect. Part of this work was performed in collaboration with S.-W. Cheong (Rutgers Univ.), D. Talbayev (Tulane Univ.) and V. Kiryukhin (Rutgers Univ).