Continuous progress in the development of light sources for the generation of tunable ultrashort pulses from the near-infrared to all the visible range provides a very efficient tool for spectroscopic techniques able to follow ultrafast dynamical processes in matter. Second-order nonlinear optical processes like Optical Parametric Amplification (OPA) have demonstrated the capability of generating light pulses with durations down to few cycles of the carrier wave. The aim of this paper is to introduce the basic concepts for the generation of tunable ultrashort pulses and show their application to ultrafast spectroscopy. We will discuss the principles of parametric amplification and the main criteria for the design of broad-band OPAs; we will also illustrate some of the schemes providing ultrashort pulses in the spectral ranges from the ultraviolet to the infrared, offering a comprehensive overview of the state of the art of the current research activity in this rapidly evolving field. An important requirement for the applications of ultrashort pulses is the capability to measure the amplitude and phase of their electric field; we will discuss a rich ensemble of spectrographic, interferometric or phase-scanning techniques for the temporal characterization of ultrashort pulses. Pump-probe techniques with broadband pulses and more recently two-dimensional spectroscopic techniques allow to follow in great detail complex dynamical processes. The few examples reported in this review just provide a sample of what is already a vast class of ultrafast phenomena, which can be studied nowadays in real time.