Strong optical pulses at mid-infrared and terahertz frequencies have recently emerged as a powerful tool to manipulate and control the solid state and especially complex condensed matter systems with strongly correlated electrons. The recent developments in high-power sources in the 0.1-30 THz frequency range, both from table-top laser systems and Free-Electron Lasers, has provided access to excitations of molecules and solids, which can be stimulated at their resonance frequencies. Amongst these, we discuss free electrons in metals, superconducting gaps and Josephson plasmons in layered superconductors, vibrational modes of the crystal lattice (phonons), as well as magnetic excitations. This Review provides an overview and illustrative examples of how intense THz transients can be used to resonantly control matter, with particular focus on strongly correlated electron systems and high-temperature superconductors.