The cosmic star-formation history has been significantly advanced by multiwavelength imaging and spectroscopic surveys over the past two decades. This review outlines the techniques and theoretical tools that allow astronomers to map the history of star formation, heavy element production, and reionization from the cosmic "dark ages" to the present. A consistent picture emerges showing that the star-formation rate density peaked around 3.5 Gyr after the Big Bang at z ≈ 1.9, then declined exponentially with an e-folding timescale of 3.9 Gyr. Half of today's stellar mass was formed before z = 1.3, with 25% formed before the peak and 25% after z = 0.7. Less than 1% of today's stars formed during reionization. Under a universal initial mass function, the global stellar mass density matches the time integral of all preceding star-formation activity. The comoving rates of star formation and black hole accretion follow a similar rise and fall, indicating co-evolution of black holes and their host galaxies. The mean metallicity of the Universe rose to about 0.001 solar by z = 6, accompanied by fewer than ten hydrogen Lyman-continuum photons per baryon, a tight budget for reionization. The review discusses the equations of cosmic chemical evolution, measuring mass from light, star-formation rates, and the state of the art in galaxy studies. It highlights the importance of understanding the cosmic star-formation history, including the role of the initial mass function, metallicity, and the evolution of black holes. The review also addresses the challenges in interpreting galaxy data, the impact of dust extinction, and the use of various observational techniques to determine star-formation rates and stellar masses. The conversion factors between FUV luminosity and star-formation rates are discussed, with a focus on the effects of metallicity and redshift. The review concludes with the importance of understanding the cosmic star-formation history in the context of galaxy evolution and the role of dark matter.The cosmic star-formation history has been significantly advanced by multiwavelength imaging and spectroscopic surveys over the past two decades. This review outlines the techniques and theoretical tools that allow astronomers to map the history of star formation, heavy element production, and reionization from the cosmic "dark ages" to the present. A consistent picture emerges showing that the star-formation rate density peaked around 3.5 Gyr after the Big Bang at z ≈ 1.9, then declined exponentially with an e-folding timescale of 3.9 Gyr. Half of today's stellar mass was formed before z = 1.3, with 25% formed before the peak and 25% after z = 0.7. Less than 1% of today's stars formed during reionization. Under a universal initial mass function, the global stellar mass density matches the time integral of all preceding star-formation activity. The comoving rates of star formation and black hole accretion follow a similar rise and fall, indicating co-evolution of black holes and their host galaxies. The mean metallicity of the Universe rose to about 0.001 solar by z = 6, accompanied by fewer than ten hydrogen Lyman-continuum photons per baryon, a tight budget for reionization. The review discusses the equations of cosmic chemical evolution, measuring mass from light, star-formation rates, and the state of the art in galaxy studies. It highlights the importance of understanding the cosmic star-formation history, including the role of the initial mass function, metallicity, and the evolution of black holes. The review also addresses the challenges in interpreting galaxy data, the impact of dust extinction, and the use of various observational techniques to determine star-formation rates and stellar masses. The conversion factors between FUV luminosity and star-formation rates are discussed, with a focus on the effects of metallicity and redshift. The review concludes with the importance of understanding the cosmic star-formation history in the context of galaxy evolution and the role of dark matter.