Heatlines were proposed in 1983 by Kimura and Bejan (1983) as adequate tools for visualization and analysis of convection heat transfer. The masslines, their equivalent to apply to convection mass transfer, were proposed in 1987 by Trevisan and Bejan. These visualization and analysis tools proved to be useful, and their application in the fields of convective heat and/or mass transfer is still increasing. When the heat function and/or the mass function are made dimensionless in an adequate way, their values are closely related with the Nusselt and/or Sherwood numbers. The basics of the method were established in the 1980(s), and some novelties were subsequently added in order to increase the applicability range and facility of use of such visualization tools. Main steps included their use in unsteady problems, their use in polar cylindrical and spherical coordinate systems, development of similarity expressions for the heat function in laminar convective boundary layers, application of the method to turbulent flow problems, unification of the streamline, heatline, and massline methods (involving isotropic or anisotropic media), and the extension and unification of the method to apply to reacting flows. The method is now well established, and the efforts made towards unification resulted in very useful tools for visualization and analysis, which can be easily included in software packages for numerical heat transfer and fluid flow. This review describes the origins and evolution of the heatlines and masslines as visualization and analysis tools, from their first steps to the present.