Mechanical and electromagnetic waves are commonly used in nondestructive testing (NDT) techniques for evaluating the materials and structures in civil engineering industry, due to their good examination of defects inside the matter. However, the individual use of mechanical wave or electromagnetic wave in NDT methods sometimes does not fulfill the satisfactory detection in practice because of the operational inconvenience and low sensitivity. It has been demonstrated that the combination of using both types of waves can achieve a better performance for NDT application and would be the future direction for defect detection, as the advantages of each physical wave are picked out whereas the weaknesses are mitigated. This paper discusses the fundamental mechanisms and the current applications of using mechanical and electromagnetic waves for defect detection, with the goal of providing the physical knowledge and the perspectives of developing the NDT applications with these two types of waves. Typical mechanical-wave-based NDT methods such as acoustic emission, ultrasonic technique, and impact-echo method are reviewed. In addition, NDT methods using electromagnetic wave, which include optical fiber sensing technique, laser speckle interferometry and laser reflection technique are discussed. Advantages and disadvantages of these methods are outlined. In particular, we focus on a recent NDT method called acoustic-laser technique, which utilizes both the mechanical and electromagnetic waves. The basic principles and some important experimental data recorded by the acoustic-laser technique are described and its future development in the field of defect detection in civil infrastructure is presented.