This review discusses the techniques and theoretical tools used to map the cosmic history of star formation, heavy element production, and reionization from the early universe to the present. Key findings include: 1. **Star Formation Rate Density (SFRD)**: The SFRD peaked approximately 3.5 billion years after the Big Bang, at a redshift of about 1.9, and declined exponentially with an e-folding time of 3.9 billion years. Half of the stellar mass observed today was formed before a redshift of 1.3. 2. **Galaxy Evolution**: The global stellar mass density matches well with the time integral of all preceding star formation activity, assuming a universal initial mass function (IMF). The comoving rates of star formation and central black hole accretion follow similar trends, suggesting co-evolution between black holes and their host galaxies. 3. **Metallicity Evolution**: The mean metallicity of the universe increased to about 0.001 solar by a redshift of 6, one billion years after the Big Bang. This increase was accompanied by the production of fewer than ten hydrogen Lyman-continuum photons per baryon, indicating a tight budget for cosmological reionization. 4. **Galaxy Taxonomy**: The review highlights the challenges in understanding galaxy taxonomy due to the complex evolutionary phases of individual galaxy subpopulations. However, the use of multiwavelength surveys has enriched our understanding of galaxy properties, such as colors, surface brightnesses, and concentrations. 5. **Stellar Population Synthesis**: The review discusses the importance of stellar population synthesis models in inferring star formation rates and stellar masses from observed light. These models help account for the effects of dust extinction, IMF variations, and metallicity evolution. 6. **Cosmic Chemical Evolution**: The equations of cosmic chemical evolution are presented, governing the consumption of gas into stars and the formation and dispersal of heavy elements. The return fraction and net metal yield are key parameters that determine the evolution of heavy element abundance in the universe. 7. **Observational Techniques**: The review covers various observational techniques, including UV, IR, submillimeter, and radio observations, and their sensitivity to different stellar masses and ages. The use of stellar population synthesis models to convert observed light into physical properties is discussed. 8. **Future Directions**: The review concludes with a discussion of ongoing challenges and future research directions, emphasizing the need for more comprehensive models and observations to fully understand the cosmic history of star formation and galaxy evolution.This review discusses the techniques and theoretical tools used to map the cosmic history of star formation, heavy element production, and reionization from the early universe to the present. Key findings include: 1. **Star Formation Rate Density (SFRD)**: The SFRD peaked approximately 3.5 billion years after the Big Bang, at a redshift of about 1.9, and declined exponentially with an e-folding time of 3.9 billion years. Half of the stellar mass observed today was formed before a redshift of 1.3. 2. **Galaxy Evolution**: The global stellar mass density matches well with the time integral of all preceding star formation activity, assuming a universal initial mass function (IMF). The comoving rates of star formation and central black hole accretion follow similar trends, suggesting co-evolution between black holes and their host galaxies. 3. **Metallicity Evolution**: The mean metallicity of the universe increased to about 0.001 solar by a redshift of 6, one billion years after the Big Bang. This increase was accompanied by the production of fewer than ten hydrogen Lyman-continuum photons per baryon, indicating a tight budget for cosmological reionization. 4. **Galaxy Taxonomy**: The review highlights the challenges in understanding galaxy taxonomy due to the complex evolutionary phases of individual galaxy subpopulations. However, the use of multiwavelength surveys has enriched our understanding of galaxy properties, such as colors, surface brightnesses, and concentrations. 5. **Stellar Population Synthesis**: The review discusses the importance of stellar population synthesis models in inferring star formation rates and stellar masses from observed light. These models help account for the effects of dust extinction, IMF variations, and metallicity evolution. 6. **Cosmic Chemical Evolution**: The equations of cosmic chemical evolution are presented, governing the consumption of gas into stars and the formation and dispersal of heavy elements. The return fraction and net metal yield are key parameters that determine the evolution of heavy element abundance in the universe. 7. **Observational Techniques**: The review covers various observational techniques, including UV, IR, submillimeter, and radio observations, and their sensitivity to different stellar masses and ages. The use of stellar population synthesis models to convert observed light into physical properties is discussed. 8. **Future Directions**: The review concludes with a discussion of ongoing challenges and future research directions, emphasizing the need for more comprehensive models and observations to fully understand the cosmic history of star formation and galaxy evolution.