The welfare theorems assume everyone has the same information. In reality, information is almost always asymmetric — one party to a transaction knows more than the other. This asymmetry creates some of the most important market failures in economics.
Asymmetric information comes in two forms. Hidden characteristics (adverse selection) occur before a transaction. Sellers of used cars know more about quality than buyers. Sick people are more likely to buy health insurance than healthy people. This information gap can cause markets to unravel: if buyers assume average quality and price accordingly, the best sellers leave the market, quality drops further, more sellers leave, and the market collapses. George Akerlof's "Market for Lemons" (1970) earned him the Nobel Prize for formalizing this insight.
Moral hazard (hidden actions) occurs after a transaction. Once you have insurance, you may take less care. Once a manager is hired, they may shirk. The problem is that the principal (the insurance company, the employer) cannot perfectly observe the agent's behavior. Solutions include deductibles, performance pay, monitoring, and efficiency wages.
Signaling is how the informed party communicates their type. A college degree may not teach useful skills, but completing one signals intelligence and discipline to employers. For a signal to work, it must be costly to fake — otherwise everyone would do it. Michael Spence's job market signaling model explains why education can increase wages even if it does not increase productivity.
Screening is the reverse: the uninformed party designs a menu of contracts to sort different types. Insurance companies offer plans with different deductibles; high-risk customers choose low deductibles, revealing their type.
These concepts explain phenomena across economics: why warranties exist, why banks require collateral, why firms pay above-market wages, and why government regulation of financial markets is necessary.