Who regulates them?
Insurance companies in the United States are primarily regulated by the individual states. There is no one Federal regulatory agency (such as the Securities and Exchange Commission that has a central role in regulating the securities industry, or the Comptroller of the Currency who oversees national banks) that specifically oversees insurance companies. The name of the state insurance regulatory agency typically is the "Insurance Department", "Division of Insurance," "Insurance Bureau" or something similar. The agencies are typically headed by a state government official usually called the "Commissioner of Insurance", "Superintendent of Insurance" or "Director of Insurance", or something similar. In most states that person is appointed by the Governor, although in some states, including California, the "Insurance Commissioner" is an elected office.
Each state assumes primary responsibility for overseeing the financial operations and management of insurance companies that are incorporated in that state. For example, Prudential was incorporated in New Jersey, so that state has a primary role in its regulation, while Metropolitan is incorporated in New York, which has the primary role. (Companies have their "statutory home office" -- even though sometimes it is just a mail drop -- in the state that incorporated them.) Each state also regulates the local operations of the insurance companies it has licensed to do business within the state, particularly as they relate to policy forms, rates, sales agents and their practices.
To coordinate the regulatory processes for each of the 50 states and the District of Columbia, Puerto Rico and the US Virgin Islands, there is the National Association of Insurance Commissioners, made up of the states' insurance regulators, who do cooperate (more or less) in developing a common form of financial statement, oversight teams, and model laws which the states' legislatures then sometimes enact, and model regulations which the regulators sometimes adopt.
Most states have laws regulating the conduct of insurance business to ensure fairness in the way companies deal with applicants for insurance and policyholders. One of the functions of a Department of Insurance is to enforce these so-called "unfair trade practices" and "unfair claims practices" laws by investigating complaints by consumers and taking action, when appropriate, to get companies to stop conduct that violates the laws and impose penalties for violations. Other duties of a Department of Insurance include reviewing and approving the policy forms used by insurance companies and approving rates charged for various types of insurance to assure compliance with state laws that regulate insurance rates.