In recent years, algorithmic-based market manipulation in stock and power markets has considerably increased, and it is difficult to identify all such manipulation cases. This causes serious challenges for market regulators. This work highlights and lists various aspects of the monitoring of stock and power markets, using as test cases the regulatory agencies and regulatory policies in diverse regions, including Hong Kong, the United Kingdom, the United States and the European Union. Reported cases of market manipulations in the regions are examined. In order to help establish a relevant digital regulatory system, this work reviews and categorizes the indicators used to monitor the stock and power markets, and provides an in-depth analysis of the relationship between the indicators and market manipulation. This study specifically compiles a set of 10 indicators for detecting manipulation in the stock market, utilizing the perspectives of return rate, liquidity, volatility, market sentiment, closing price and firm governance. Additionally, 15 indicators are identified for detecting manipulation in the power market, utilizing the perspectives of market power (also known as pricing power or market structure), market conduct and market performance. Finally, the study elaborates on the current challenges in the regulation of stock and power markets in terms of parameter performance, data availability and technical requirements.