The design of multi-item mechanisms is considered one of the most important problems in the field of algorithmic game theory. Optimal welfare or revenue maximization mechanisms in a multi-item setting can be complicated and have many unnatural behaviors that make them hard to analyze and implement. Participants in complicated mechanisms may also get confused and have unpredictable behaviors. Thus, designing simple and approximately optimal mechanisms is desirable. This thesis discusses the power of posted pricing mechanisms, the most ubiquitous class of simple mechanisms applied in the real world, for buyers with weak or even no distributional assumptions. We study two settings where the mechanism designer wants to maximize the revenue or social welfare. For revenue maximization, it is known that the revenue gap between optimal randomized mechanisms and item pricings can be unbounded in the single-buyer setting. In this thesis, we challenge such a conventional belief by showing that if the buyer is allowed to interact with the mechanism for multiple times, such a large gap reduces to logarithmic in the number of items. Such a result holds for the most general setting possible, with an arbitrarily correlated distribution of buyer types and arbitrary valuations. When the buyer's valuation has some ordering structure, the competitive ratio achieved by item pricing can be improved, and the near-optimal item pricing becomes tractable. For welfare maximization, we study a broad class of online resource allocation settings motivated by applications to cloud economics. When buyers arrive over time and desire bundles of items, selling bundles at static and anonymous prices is the asymptotically optimal welfare-maximization mechanism. No other online algorithm, even one that does not need to satisfy incentive compatibility, can achieve better asymptotic performance.