Sandwich construction is defined as a structure consisting of two thin face sheets adhered to a thick layer of low-density material. These substances are referred to as the core material and are an important component of the sandwich composite including rigid foam, honeycomb, wood, truss, or lattice. Cellular foams are mostly polymer plastics, but can also be metal, carbon, and ceramics. Honeycombs consist of usually aluminum, thermoplastic, paper, synthetic fiber paper, and composite sheets. Natural-based core comes from balsa trees, and other light woods, such as paulownia, cork, and bamboo have been used. Other cores, made by fabrics and textiles, have different functions in the composite industries. In this chapter, the processing method of different core materials will be introduced briefly; the special features and typical properties of each core will be discussed, and the common formats of the core materials will be presented. Also, the applications of each core in the sandwich composite industries will be revealed. Materials presented have been used in a variety of applications (not just R&D projects) and are commercially available. This chapter gives readers a complete picture of the core materials and understand the origin, development, characteristics, and applications of each core material.