Reconfigurable metamaterials have emerged as promising platforms for manipulating the spectral and spatial properties of terahertz waves without being limited by the characteristics of naturally existing materials. Here, we present a comprehensive overview of various types of reconfigurable metamaterials that are utilized to manipulate the intensity, phase, polarization, and propagation direction of terahertz waves. We discuss various reconfiguration mechanisms based on optical, electrical, thermal, and mechanical stimuli while using semiconductors, superconductors, phase-change materials, graphene, and electromechanical structures. The advantages and disadvantages of different reconfigurable metamaterial designs in terms of modulation efficiency, modulation bandwidth, modulation speed, and system complexity are discussed in detail.