This paper provides a comprehensive review of equity trading simulators, focusing on their performance in assuring pre-trade compliance and portfolio investment management. A systematic search was conducted that covered the period of January 2000 to May 2023 and used keywords related to equity trade simulators, portfolio management, pre-trade compliance, online trading, and artificial intelligence. Studies demonstrating the use of simulators and online platforms specific to portfolio investment management, written in English, and matching the specified query were included. Abstracts, commentaries, editorials, and studies unrelated to finance and investments were excluded. The data extraction process included data related to challenges in modern portfolio trading, online stock trading strategies, the utilization of deep learning, the features of equity trade simulators, and examples of equity trade simulators. A total of 32 studies were included in the systematic review and were approved for qualitative analysis. The challenges identified for portfolio trading included the subjective nature of the inputs, variations in the return distributions, the complexity of blending different investments, considerations of liquidity, trading illiquid securities, optimal portfolio execution, clustering and classification, the handling of special trading days, the real-time pricing of derivatives, and transaction cost models (TCMs). Portfolio optimization techniques have evolved to maximize portfolio returns and minimize risk through optimal asset allocation. Equity trade simulators have become vital tools for portfolio managers, enabling them to assess investment strategies, ensure pre-trade compliance, and mitigate risks. Through simulations, portfolio managers can test investment scenarios, identify potential hazards, and improve their decision-making process.