Algorithmic mechanism design is an interdisciplinary field, concerned with the design of algorithms that are used by strategic agents. This field has applications in many real-world settings, such as auction design, search problems, and matching markets. In this thesis we study the mechanisms in these areas through lenses of simplicity and practicality. We pursue two main directions: study the strength of simple mechanisms, and improve the efficiency of practical mechanisms. In auction design, we consider a setting where a seller wants to sell many items to many buyers, and establish a tight gap between the efficiency of a simple and commonly-used auction with the complicated revenue-optimal auction. In search theory context, we introduce Pandora's problem with alternative inspections and provide the first approximately-optimal mechanism for this problem. In Pandora's problem with alternative inspections, a searcher wants to select one out of n elements whose values are unknown ahead of time. The searcher evaluates the elements one by one and can choose among different costly ways to evaluate each element, the order to evaluate the elements, and how long to continue the search, in order to maximize her utility. In matching markets, we propose theoretical models that closely capture the participant behaviors in the real world, and provide methods to optimize the already implemented mechanisms.