Undesired conversion between common-mode (CM) and differential-mode (DM) noise often occurs in modern electronic and electrical systems, posing challenges in terms of Electromagnetic Compatibility (EMC). Modal analysis represents a crucial tool in EMC investigation and provides insight into the mechanism underlying mode conversion. By inspecting CM and DM behaviors and their interconversion, it allows for understanding of conducted emission propagation mechanisms, drives electromagnetic interference (EMI) filter design towards optimal/tailored solutions, and enables the possibility to identify the main contributors to the radiated emission phenomenon. This paper offers a comprehensive review of mathematical methodologies and modelling strategies for EMC-oriented modal analysis, with particular emphasis on mode conversion phenomena. To this end, modal decomposition techniques and standard parameters for quantifying mode conversion are summarized and compared. Additionally, the paper provides an overview and in-depth discussion of different scenarios and test cases in which mode conversion occurs, with the final goal to achieve a systematic comprehension of its root causes and consequences within power and communication systems. Eventually, a survey of circuit modelling approaches for mode conversion is presented, offering insights into addressing this phenomenon effectively.