Low-energy elementary excitations such as phonons, excitons, magnons or energy gaps insemiconductor nanostructures and strongly correlated materials are of central importance for solid-state physics. The frequency window between 1 THz and 100 THz comprises most of these resonances. Over the last years, phase-locked light pulses in the ultrabroadband terahertz spectral domain have evolved into a powerful tool for probing these excitations directly via the amplitude of the light field and on a sub-cycle time scale. Latest advances of intense multi-THz sources generating peak electric and magnetic fields as high as 108 MV/cm and 30 T, respectively, have now facilitated the important step from mere observation to coherent control of low-energy dynamics by intense THz transients. After an introduction to the technology, typical examples of ultrabroadband and nonlinear THz studies on complex materials, as well as first steps towards new areas of quantum optics are presented: Sub-cycle analysis of electronic and lattice degrees of freedom after electronic excitation of VO2 and YBa2Cu3O7-δ, coherent switching of spin waves in NiO via the magnetic field component and non-adiabatic THz quantum optics controlling light-matter interaction in the ultrastrong coupling regime.