The Generalized Differential Quadrature (GDQ) method has been widely used in scientific and engineering computation. Its first applications were related to fluid mechanics. Nevertheless, it has been employed soon in structural engineering for solving different problems, such as thermal, acoustics, vibrations, flows in porous media and so on. The main advantage of the GDQ method is that it can be easily applied to any field governed by partial differential equations, because the approximation and implementation of partial differential equations is easy and straightforward. Moreover, it is well known to be fast and reliable if compared to the classic Finite Element Method. The GDQ method was considered also in time-domain problems and for approximating integrals. Thus, the so-called Generalized Integral Quadrature (GIQ) method was introduced. Thanks to their great versatility, the GDQ and GIQ methods were implemented and used by a lot of researchers for investigating several fields of avant-garde nature. Nowadays, the GDQ method is particularly used in structural mechanics for investigating the static and dynamic behavior of systems made of composite and advanced materials, which are generally complex to study numerically, but they become easy to implement and analyze through this numerical technique. These applications are related, but not limited to, SMART composite structures, carbon-nano tubes reinforced composites, carbon-reinforced polymer composites, functionally graded materials, and numerical optimization of composite structures. The Special Issue of Applied Sciences “Applications of Generalized Differential and Integral Quadrature Methods” aims to cover recent advances in the development of engineering, mathematical and physical applications of Generalized Differential Quadrature methods. Moreover, this special issue is aimed at new researchers in this field, who wants to learn the main novelties and applications related to these numerical techniques.