Structural damages occur in modern structures during operations due to environmental and human factors. The damages accumulating with time may lead to a significant decrease in structure performance or even destruction; natural symmetry is broken, resulting in an unexpected life and economic loss. Therefore, it is necessary to monitor the structural response to detect the damage in an early stage, evaluate the health condition of structures, and ensure the operation safety of structures. In fact, the structure and the evaluation can be considered as a special symmetry. Among several SHM methods, vibration-based SHM techniques have been widely adopted recently. Hence, this paper reviews the vibration-based SHM methods in terms of the vibrational parameters used. In addition, the technical codes on vibration based SHM system have also been reviewed, since they are more important in engineering applications. Several related ISO standards and national codes have been developed and implemented, while more specific technical codes are still required to provide more detailed guidelines in practice to maintain structure safety and natural symmetry.