Recently, the penetration of renewable energy sources (RESs) into electrical power systems is witnessing a large attention due to their inexhaustibility, environmental benefits, storage capabilities, lower maintenance and stronger economy, etc. Among these RESs, offshore wind power plants (OWPP) are ones of the most widespread power plants that have emerged with regard to being competitive with other energy technologies. However, the application of power electronic converters (PECs), offshore transmission lines and large substation transformers result in considerable power quality (PQ) issues in grid connected OWPP. Moreover, due to the installation of filters for each OWPP, some other challenges such as voltage and frequency stability arise. In this regard, various customs power devices along with integration control methodologies have been implemented to deal with stated issues. Furthermore, for a smooth and reliable operation of the system, each country established various grid codes. Although various mitigation schemes and related standards for OWPP are documented separately, a comprehensive review covering these aspects has not yet addressed in the literature. The objective of this study is to compare and relate prior as well as latest developments on PQ and stability challenges and their solutions. Low voltage ride through (LVRT) schemes and associated grid codes prevalent for the interconnection of OWPP based power grid have been deliberated. In addition, various PQ issues and mitigation options such as FACTS based filters, DFIG based adaptive and conventional control algorithms, ESS based methods and LVRT requirements have been summarized and compared. Finally, recommendations and future trends for PQ improvement are highlighted at the end.