Ultrafast spectroscopy techniques use sequences of ultrashort light pulses (with femto- to attosecond durations) to study photoinduced dynamical processes in atoms, molecules, nanostructures, and solids. This field of research has experienced an impetuous growth in recent years, due to the technological progress in the generation of ultrashort light pulses and to the development of sophisticated spectroscopic techniques, which greatly increase the amount of information on the process under study. This paper aims at providing a non exhaustive overview of the state of the art of the field and at pointing out future challenges. We first review the progress in ultrafast optics, which has enabled the generation of broadly tunable light pulses with duration down to a few optical cycles; we then discuss the pump probe technique, showing examples of its capability to combine very high time resolution, down to the attosecond regime, with broad spectral coverage; we introduce two-dimensional spectroscopy and present results that demonstrate the additional information content provided by the combination of temporal and spectral resolution. Next, we review the achievements of ultrafast X-ray and electron diffraction, which provide time-dependent structural information on photochemical processes, and we conclude with a critical analysis of the future open challenges in the field.