In recent years, multistable metastructures have emerged as a central focus in research on smart materials and reconfigurable structures. These structures, with their ability to transition controllably among multiple stable states, enable the design of lightweight, adaptable, and programmably reconfigurable systems. Advances in additive manufacturing, particularly Fused Filament Fabrication (FFF) 3D printing, have opened new pathways for precise engineering of multistable behavior and for controlling geometric parameters, material arrangements, and residual stresses. The primary approaches to achieving multistability include the design of compliant mechanisms, the use of specific cellular arrangements, and integrated fabrication via 3D printing. These strategies facilitate large deformations, sequences of snap-through events, and controlled energy storage. The influence of additive manufacturing parameters, such as layer orientation and thickness, infill density, and thermal conditions, on the number of stable states and energy well depths has been demonstrated. This review article discusses design principles, activation mechanisms, the role of cellular architecture, and the impact of printing process parameters on the development of multistable metastructures, providing a comprehensive framework for understanding and advancing this field.