Oscillators are the subjects of intensive research. From Colpitts oscillators to phase locked loops, methods have been proposed to improve stability, frequency resolution, and spectral purity. Among the all-digital approaches, direct digital frequency synthesis are now available as integrated circuits and they output waveforms up to hundreds of megahertz. While DDS is slowly gaining acceptance in new system designs, methods used to improve the quality of the generated waveform are seldom used, even nowadays. The purpose of this article is to give an overview of the basics of DDS, along with simple formulas to compute bounds of the signal characteristics. Moreover, several methods, some patented, are presented to overcome some of the limits of the basic DDS with a focus on improving output signal quality.