The discovery of molecular single crystals that display interesting elastic behaviour has generated excitement regarding their potential applications as it has upended the common perception of crystals as brittle objects. In order to design new functional materials based on molecular crystals, a comprehensive understanding of how these materials respond to deformation on a molecular-level is required. An introduction to the underlying mechanical theory and how it may be applied to single crystals is provided, along with a comprehensive discussion on how these mechanical properties can be characterised. While this field has already presented a large number of elastically flexible crystals, there is a lack of detailed mechanical characterisation data and some contention regarding the atomic-scale mechanism of elasticity. Due to the discrepancies and contradictions between theories proposed in the literature, it is not yet understood why some crystals are elastic while others shatter under applied force. To dispel ambiguity and guide future research, a set of criteria are proposed to define an elastically flexible crystal, so that these materials may find applications among future technologies.