In the voltage source power electronic converter, DC-link capacitors usually work as buffering elements between the DC and AC sides. The high failure rate and large space occupied by the DC-link capacitors directly affect the reliability and power density of the converters. The analysis and calculation of the DC-link capacitor current is crucial to achieve the refined design of converters. In this work, the analysis and calculation methods of DC-link capacitor current are divided into three categories, according to the calculation principle, namely, simulation method, RMS analysis method, and spectral analysis method, and their calculation methods are summarized. First, the types of capacitors and their characteristics are briefly introduced. Second, the three-phase two-level converter is taken as an example to introduce the basic principles, calculation steps, application scope, advantages, and disadvantages of the latter two methods in detail, as well as the influence of non-ideal factors, such as the output ripple on the calculation results. This work also discusses the calculation of the multi-level converter’s DC-link capacitor current spectrum and the current characteristics of multi-phase converters, which are rarely reported. Third, the problem of resonance between the DC-link capacitors and the DC bus inductor is introduced. For the distributed arrangement of multiple DC-link capacitors on DC bus converters, this study proposes a method based on a constant current source equivalent circuit, which can accurately calculate the DC-link capacitor current spectrum that is affected by loop current and resonance. Finally, the current problems and future directions of the DC-link capacitor design are pointed out.