Book excerpt: Emerging from electromagnetic waves and fast extending to acoustic and elastic waves, metamaterials that exhibit extraordinary wave control abilities have been gaining soaring attention. Over the past two decades, elastic metamaterials with engineered microstructures have provided a variety of appealing solutions for controlling elastic waves and vibrations. By tailoring their internal microstructures at a subwavelength scale, elastic metamaterials fruitfully distinct themselves from traditional materials or phononic crystals by their striking functions in wave trajectory manipulation, cloaking, nonreciprocal and topological wave control, as well as low-frequency wave/vibration mitigation and absorption.