In this talk, we discuss the opportunities and potentials of metamaterials in which their constituent elements are modulated in space and time with tailored patterns, or abruptly change in space-time, in order to overcome the constraints of passive, linear, time-invariant materials. We will discuss nonreciprocal and parametric phenomena enabled by these spatiotemporally modulated metamaterials, and emphasize the challenges in efficiently modeling their responses with analytical and numerical techniques. We will also survey several applications of this platform from radio-wave and mm-wave technology to classical and quantum photonics.