Material failure may occur in a variety of situations dependent on stress conditions, temperature, and internal or external load conditions. Many of the latest engineered materials combine several material types i.e., metals, carbon, glass, resins, adhesives, heterogeneous and nanomaterials (organic/inorganic) to produce multilayered, multifaceted structures that may fail in ductile, brittle, or both cases. Mechanical testing is a standard and basic component of any design and fabricating process. Mechanical testing also plays a vital role in maintaining cost-effectiveness in innovative advancement and predominance. Destructive tests include tensile testing, chemical analysis, hardness testing, fatigue testing, creep testing, shear testing, impact testing, stress rapture testing, fastener testing, residual stress measurement, and XRD. These tests can damage the molecular arrangement and even the microstructure of engineered materials. Nondestructive testing methods evaluate component/material/object quality without damaging the sample integrity. This review outlines advanced nondestructive techniques and explains predominantly used nondestructive techniques with respect to their applications, limitations, and advantages. The literature was further analyzed regarding experimental developments, data acquisition systems, and technologically upgraded accessory components. Additionally, the various combinations of methods applied for several types of material defects are reported. The ultimate goal of this review paper is to explain advanced nondestructive testing (NDT) techniques/tests, which are comprised of notable research work reporting evolved affordable systems with fast, precise, and repeatable systems with high accuracy for both experimental and data acquisition techniques. Furthermore, these advanced NDT approaches were assessed for their potential implementation at the industrial level for faster, more accurate, and secure operations.