In many cases, the core plays a prominent role in sandwich structures. Due to the increased demand in modern engineering, many scientists are attracted to studying more about lightweight mechanical components; hence they argued that an appropriate core layer might reduce the weight of sandwich structures. Cellular structures have been noticed for their low density/weight, high strength, and high energy and sound absorption. Nowadays, due to the extreme properties of cellular structures, they are primarily used in engineering assemblies. Also, their mechanical properties could be changed by defining thickness-dependent relations for the definition of Young's modulus and density, making them more exciting for researchers. Due to the pores in these structures and, accordingly, low stiffness, it is advisable to integrate them. One of the ways to reach this aim is to use and bond two stiffer layers on their upper and lower surfaces that are called facesheets. These faces would be made from smart materials or nanocomposites in some applications. The usage of these kinds of structures has been growing in applications ranging from aerospace structures, bridge constructions, marine industry, medical science as bone tissue engineering, and products of automobile systems. This paper aims to provide a state-of-the-art review of different types of cellular sandwich structures that have been designed for high-strength and lightweight applications. Furthermore, this review investigates their performance in different structures such as beams, plates, and shells in various environmental conditions. The review shows no work is available on this topic in the literature and does not cover any particular sandwich engineering design.