This paper provides a comprehensive review of the control approaches and the power-decoupling topologies to mitigate 2ω-ripple problem in the single-phase inverters, its solutions, and discusses open challenges yet to be addressed. The cause and effects of 2ω-ripple problem and its solution based on the passive and active power-decoupling techniques are discussed. A subcategory of the active power-decoupling technique nominated as the control-oriented compensation technique is reviewed in detail, this technique can achieve the ripple-mitigation at the source through the control but not necessarily adds extra circuit or active filter to the system. The control-oriented compensation techniques can be applied in the two-stage DC-DC-AC converters and the single-stage inverters having a front-end control capability with the H-bridge such as in the quasi-switched-boost inverters. The merits and associated challenges of these techniques are listed and summarized in a tabular form. Finally, a conclusive discussion with open challenges is presented. © 2013 IEEE.