It is known that in the design of quieter mechanical systems, vibration and noise control play important roles. Recently, acoustic black holes have been effectively used for structural design in controlling vibration and noise. An acoustic black hole is a power-law tapered profile to reduce phase and group velocities of wave propagation to zero. Additionally, the vibration energy at the location of acoustic black hole increases due to the gradual reduction of its thickness. The vibration damping, sound reduction, and vibration energy harvesting are the major applications in structural design with acoustic black holes. In this paper, a review of basic theoretical, numerical, and experimental studies on the applications of acoustic black holes is presented. In addition, the influences of the various geometrical parameters and the configuration of acoustic black holes are presented. The studies show that the use of acoustic black holes results in an effective control of vibration and noise. It is seen that the acoustic black holes have a great potential for quiet design of complex structures.