As structures become thinner and lighter to conserve materials, they become more compliant and prone to vibration. These structures may also not be able to support a traditional vibration control system with concentrated control forces. Elastic metamaterials (EMMs) consist of distributed resonators, small compared to the wavelength of vibration, and offer a potential solution. Such metamaterials also offer an opportunity to control vibration in the presence of uncertainty, by distributing the resonator tuning frequencies. This thesis investigates the use of EMMs for robust vibration control.In the first instance, different optimisation algorithms are investigated for the tuning of an EMM for the robust control of vibration. A particle swarm optimisation (PSO) is shown to achieve similar performance compared to both a more complex genetic algorithm (GA) and a hybrid genetic algorithm (HGA). To be able to realise an EMM with variously tuned resonators, a concept resonator is proposed, which utilises multi-material 3D inkjet printing. The dynamic response of the novel resonator design is characterised experimentally, and an EMM utilising the resonator is optimised using a PSO. The optimised EMM is validated experimentally, and it is shown that in the presence of structural uncertainty, the robustly optimised EMM outperforms a design optimised based on a nominal structure alone. A semi-active approach to EMM design is also investigated, where an impedance connected across the terminals of an electrodynamic transducer, known as shunting, is used to tune the resonance frequency and damping. An electrodynamic metamaterial (EDMM) is proposed, consisting of shunted mass-produced electrodynamic proof-mass transducers. Series resistive and inductive (RL) shunt impedances are optimised for the absorption of vibration in the presence of both structural uncertainties and realistic uncertainties in the actuators. The simulation study demonstrates the limitations of the design due to the potential for instability and the wide range of uncertainty in the transducer’s electrical parameters. An adaptive tuning algorithm is also proposed, in which an array of shunted actuators are tuned to the frequencies corresponding to the highest magnitude components of a real-time frequency analysis of the structural dynamics. Using a parallel resistive-inductive-capacitative (RLC) shunt, this approach is shown to achieve greater robustness to structural uncertainties compared to a fixed tuning and a swept tuning approach, where the resonance frequency is continuously swept between bounds.