Phononic crystals (PCs) and metamaterials (MMs) can exhibit abnormal properties, even far beyond those found in nature, through artificial design of the topology or ordered structure of unit cells. This emerging class of materials has diverse application potentials in many fields. Recently, the concept of tunable PCs or MMs has been proposed to manipulate a variety of wave functions on demand. In this review, we survey recent developments in tunable and active PCs and MMs, including bandgap and bandgap engineering, anomalous behaviors of wave propagation, as well as tunable manipulation of waves based on different regulation mechanisms: tunable mechanical reconfiguration and materials with multifield coupling. We conclude by outlining future directions in the emerging field.