Heat transfer and pressure drop correlations for fully developed laminar Newtonian fluid flow in curved and coiled circular tubes are reviewed. Curved geometry is one of the passive heat transfer enhancement methods that fits several heat transfer applications, such as power production, chemical and food industries, electronics, environment engineering, and so on. Centrifugal force generates a pair or two pairs of cross-sectional secondary flow (based on the Dean number), which are known as the Dean vortices, and improves the overall heat transfer performance with an amplified peripheral Nusselt number variation. The main purpose of this review paper is to provide researchers with a comprehensive list of correlations and concepts that they may need during their research. The paper begins with an introduction to the governing equations and important dimensionless numbers for the flow in curved tubes. The correlations for developing flow in curved and coiled circular tubes are also presented. The main contribution of this study is reviewing the numerical and experimental correlations to calculate friction factor and Nusselt number in curved circular tubes. Nusselt number correlations are categorized based on the thermal boundary condition, as well as on the method. A Dean number range of 1 to 20,000 for the pressure drop correlations and 1 to 7000 for the heat transfer correlations and a Prandtl number range of 0.1 to 7,000 are covered with the reviewed correlations.