Metamaterials are artificial materials with properties well beyond what offered by nature, providing unprecedented opportunities to tailor and enhance the control of waves. In this course, we will discuss the unusual properties of metamaterials for electromagnetics and acoustics, showing how suitably tailored meta-atoms and their arrangements open exciting venues for cloaking and scattering suppression, nonreciprocity and topological phenomena without magnetic bias, and giant nonlinear effects at subwavelength scales. Physical insights into the underlying physics, modeling and homogenization techniques, and new devices and functionalities based on these concepts will be discussed.