Power laws are prevalent in economics and finance, describing surprising empirical regularities. This paper surveys well-documented power laws in income, wealth, city and firm sizes, stock returns, trading volume, trade, and executive pay. It reviews theoretical mechanisms that predict power laws without requiring fine-tuning of model parameters, including random growth, optimization, and the economics of superstars combined with extreme value theory. Some empirical regularities lack appropriate explanations, highlighting open areas for future research. Power laws describe distributions where the probability of an event decreases as a power of the event's magnitude. They are characterized by a Pareto distribution, which has a heavy tail. Zipf's law, a specific power law, has an exponent of 1 and is observed in city sizes, income distributions, and other phenomena. Theoretical mechanisms for power laws include random growth, where proportional growth leads to a power law distribution. This is supported by the Kesten process, which shows that under certain conditions, the distribution converges to a power law. Optimization and the economics of superstars also generate power laws, as seen in the matching of talent with firms or audiences. Empirical power laws include Zipf's law for city sizes, firm sizes, income, and executive pay. Recent studies have also identified power laws in stock market activity, international trade, and other financial phenomena. These laws suggest that economic systems may have robust, detail-independent properties. The paper highlights the importance of understanding power laws in economics and finance, as they can provide insights into market behavior, risk management, and the distribution of wealth and income. Theoretical and empirical studies continue to explore the mechanisms behind these laws, aiming to explain their prevalence and implications.Power laws are prevalent in economics and finance, describing surprising empirical regularities. This paper surveys well-documented power laws in income, wealth, city and firm sizes, stock returns, trading volume, trade, and executive pay. It reviews theoretical mechanisms that predict power laws without requiring fine-tuning of model parameters, including random growth, optimization, and the economics of superstars combined with extreme value theory. Some empirical regularities lack appropriate explanations, highlighting open areas for future research. Power laws describe distributions where the probability of an event decreases as a power of the event's magnitude. They are characterized by a Pareto distribution, which has a heavy tail. Zipf's law, a specific power law, has an exponent of 1 and is observed in city sizes, income distributions, and other phenomena. Theoretical mechanisms for power laws include random growth, where proportional growth leads to a power law distribution. This is supported by the Kesten process, which shows that under certain conditions, the distribution converges to a power law. Optimization and the economics of superstars also generate power laws, as seen in the matching of talent with firms or audiences. Empirical power laws include Zipf's law for city sizes, firm sizes, income, and executive pay. Recent studies have also identified power laws in stock market activity, international trade, and other financial phenomena. These laws suggest that economic systems may have robust, detail-independent properties. The paper highlights the importance of understanding power laws in economics and finance, as they can provide insights into market behavior, risk management, and the distribution of wealth and income. Theoretical and empirical studies continue to explore the mechanisms behind these laws, aiming to explain their prevalence and implications.