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The era of modern portfolio theory began with the revolutionary approach by Harry Markowitz in 1952. However, several drawbacks of the model have rendered it impractical to be used in reality. Thus, various modifications have been done to refine the classical model, including concerns about risk measures, trading practices and computational efficiency. On the other hand, Islamic finance is proven to be a viable alternative to the conventional system following its outstanding performance during the financial crisis in 2008. This emerging sector has gained a lot of attention from investors and economists due to its significantly increasing impact on today's economy, corresponding to globalization and a demand for a sustainable investment strategy. A comprehensive literature review of the notable conventional and Islamic models is done to aid future research and development of portfolio optimization, particularly for Islamic investment. Additionally, the study provides a concisely detailed overview of the principles of Islamic finance to prepare for the future development of an Islamic finance model. Generally, this study outlines the comprehensive features of portfolio optimization models over the decades, with an attempt to classify and categorize the advantages and drawbacks of the existing models. The trend of portfolio optimization modelling can be captured by gathering and recording the problems and solutions of the reviewed models. [ABSTRACT FROM AUTHOR]