The existence of a "memory" of the previous crystalline state, which survives melting and enhances re-crystallization kinetics by a self-nucleation process, is wellknown in polymer crystallization studies. Despite being extensively investigated, since the early days of polymer crystallization studies, a complete understanding of melt memory effects is still lacking. In particular, the exact constitution of self-nuclei is still under debate. In this perspective, we provide a comprehensive and critical overview of melt memory effects in polymer crystallization. After the phenomenology of the process and some key concepts are introduced, the main experimental results of the last decades are summarized. Analogies and discrepancies of the melt memory characteristics of different polymeric systems are highlighted. Based on this background, the most significant interpretations and theories of melt memory effects are described; underlining that different interpretations may apply to various specific cases. Recent insights on self-nucleation, gained thanks to a multi-technique approach (combining calorimetry, rheology, infrared and dielectric spectroscopy), are presented. The role of intra/inter-chain segmental contacts in the strength of melt memory effects, and the differences between homopolymers and copolymers behavior, are discussed. Finally, we identify areas where further research in the field is needed to shed light on the longstanding questions regarding the origin of melt memory effects in semi-crystalline polymers.