Nonregular fractional factorial designs (FFDs) are widely used in various screening experiments for their run size economy and flexibility. In the beginning of this thesis, a brief review is given on the development of nonregular FFDs since the groundbreaking work by Hamada and Wu (1992). Then this thesis focuses on two major directions of using nonregular FFDs: analysis and construction. Some real-life examples are provided to show the correct ways to analyze nonregular FFDs, so that three potential pitfalls can be avoided. In addition, the Dantzig selector method is introduced for identifying active factors in both nonregular FFDs and supersaturated designs. Real-life examples and simulations show how ecient the Dantzig selector is when it is compared to the existing method in the literature. The quaternary code method is introduced for the construction of nonregular FFDs. The properties and uses of quaternary codes toward the construction of nonregular FFDs are explored, and optimal designs are constructed under some common criteria.