Mechanical metamaterials exhibit some superior mechanical properties such as ultrahigh strength-to-weight ratio, negative bulk-modulus, negative stiffness, negative mass-density, and negative Poisson's ratio. These advantages led to a variety of applications, especially in vibration isolation, by targeting and tuning for a specific frequency-range called stopband. The tuning ability is achieved from its array of unit-cells, which can be topologically optimized for the desired frequency range. This review discusses the development of mechanical metamaterials and focuses on its vibration control applications by using passive and active approaches for stopband enhancement and broadening the bandwidth at varying frequency-ranges.