Locational Marginal Prices (LMPs) are critical indicators in modern energy markets, representing the cost of delivering electricity at specific locations while considering the generation and transmission constraints. LMPs facilitate the transition to dynamic energy markets by providing real-time pricing signals that reflect supply and demand conditions, thereby incentivizing efficient resource allocation and encouraging investments in renewable energy sources. However, determining LMPs requires the processing of vast amounts of data, including real-time electricity demand, generation capacities, transmission line statuses, and market bids. Owing to vulnerabilities in the underlying sensors and communication infrastructure, adversaries can launch profit-driven stealthy False Data Injection Attacks (FDIAs) to manipulate LMPs. Such manipulations can have severe consequences, including inflated electricity prices, reduced market efficiency, distorted competition, and hindered integration of renewable energy sources. Although several studies have examined the operational consequences of FDIAs, their financial impact on energy market outcomes remains insufficiently explored. This work presents a comprehensive review of FDIAs aimed at manipulating LMPs, a key pricing mechanism in modern energy markets. A detailed analysis was conducted to identify vulnerabilities arising from both the energy system infrastructure and market operations. In addition, existing energy market threat models and defense mechanisms are systematically reviewed. Finally, key research gaps are identified, and future research directions are outlined to enhance the resilience of energy markets against FDIA threats.