<p>Stock market is pivotal to economical systems. It is a platform where listed stocks of companies can be bought/sold by market participants to gain profit. In 2020, the total capitalization of all markets reached $95 trillion. Within such profiting platforms, malicious attacks like stock price/market manipulation are conducted. Stock price manipulation attack refers to the strategic act of trading either a stock, a future (derivative financial contracts), or a security (financial instrument) to increase or decrease their prices. Hence, making significant profits. Manipulation types vary by sources and/or exploited methods. To detect and deter such attacks/practices, extensive research have been conducted. To further assist the future studies, in this paper, we conduct a systematic literature review to extract research articles relevant to stock price/market manipulation attacks and their state-of-art detection systems/solutions. To the best of our knowledge, this is the first systematic literature review that is based on a predefined search methodology and systematically collects the relevant articles that were published between 2011 and 2021. After applying the systematic search methodology, we extracted and surveyed 66 articles and classified them into four main detection approaches. Namely, statistical-based, Machine Learning based, system-based/artefacts, and visualization-based/observation-based. We provide a thorough comparison among the detection systems in terms of utilized datasets, leveraged features, employed optimization techniques, and applied performance measures. Our survey also identifies and discusses a set of existing research gaps such as generality of detection approaches, near/real-time detection capability, validity of real/synthesised datasets, etc. We concluded our survey by proposing several research topics and recommendations to be investigated and addressed by future works.</p>