(A) Non-potential force between two masses acting transverse ($\widehat{\phi }$) and radial ($\widehat{r}$) to the conncting spring. (B) Compressing the spring results in a radial force, while extension results into an opposite radial force. The closed cycle ($\partial A$) of deformation gives rise to the extracted work W=k^aA. (C) A continuum of springs with transverse and radial contributions can be regarded as a material with odd elasticity. (D) Deforming such a material can result in unusual behaviour, such as self-sustaining deformation waves in overdamped media. A 90° phase shift between stress and strain facilitates wave propagation. The colour gradient indicates time. The work done by a full cycle in deformation space offsets dissipation. Reprinted with permission from [55]. Copyright©2020 Springer Nature. (E) Map of the bond orientational parameter in an active crystal consisting out of cohesive spinning colloidal magnets with magnetic attraction. The crystal is knead or broken up in smaller pieces with high local hexagonal order and like orientational order. (F) The dislocations move through the crystal in a ballistic manner. Colour map same as in (E). (E, F) Reprinted with permission from [43]. Copyright©2022 Springer Nature.