The generation of sub-optical-cycle, carrier-envelope phase-stable light pulses is one of the frontiers of ultrafast optics. The two key ingredients for sub-cycle pulse generation are bandwidths substantially exceeding one octave and accurate control of the spectral phase. These requirements are very challenging to satisfy with a single laser beam, and thus intense research activity is currently devoted to the coherent synthesis of pulses generated by separate sources. In this review we discuss the conceptual schemes and experimental tools that can be employed for the generation, amplification, control, and combination of separate light pulses. The main techniques for the spectrotemporal characterization of the synthesized fields are also described. We discuss recent implementations of coherent waveform synthesis: from the first demonstration of a single-cycle optical pulse by the addition of two pulse trains derived from a fiber laser, to the coherent combination of the outputs from optical parametric chirped-pulse amplifiers.