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The rapid growth of modern economy and the increasingly high quality of human life over the last century are essentially attributed to the development of energy technologies, including the conversion, transport, storage, and utilization of energy. The transfer of thermal energy plays an instrumental role in virtually all energy related technologies. As such, exploring the fundamentals of heat transfer is of significant importance for both scientific advancement and technological development. Each of the basic heat transfer modes is governed by different length scales, understanding and engineering of which thus underpin the development of heat transfer technologies. In this dissertation, quantification and engineering of characteristic lengths in two different heat transfer mechanisms, namely, phase change heat transfer (PCHT) and radiation heat transfer, are studied.Liquid-vapor PCHT utilizes latent heat of vaporization to efficiently transport a large amount of thermal energy, which is being used in a variety of thermal energy conversion and management applications. The critical heat flux (CHF) of PCHT, either evaporation or boiling, is fundamentally limited by mass flux of the vapor departing from the liquid-vapor interface, known as the kinetic limit. This limit could be in theory greater than 1 kW cm-2 on a planar surface, but its experimental realization has remained elusive. In the first part of this dissertation, by leveraging the small length scale for heat conduction and vapor bubble departure within a thin liquid film, a new “thin film boiling” mechanism is proposed and realized by confining the boiling liquid within a microscale film on a nanoporous membrane. Superior heat transfer performance is demonstrated with a high CHF of over 1.8 kW cm-2, which is among the highest reported values for PCHT on a planar surface and is within a factor of four of the calculated theoretical kinetic limit. Furthermore, by continuously shrinking the liquid film, a universal transition from boiling to evaporation is further identified for different fluids with varying surface tension values (water, ethanol, isopropanol, and perfluorohexane), and the heat transfer characteristics of the transition points are found to be close to the kinetic limit. The limiting factors dictating the transition between the two different heat transfer modes are also elucidated.In advanced materials for high temperature thermal transport such as thermal barrier coatings for turbine blades and heat transfer media in concentrated solar power plants, the radiative thermal transport, which is often negligible at room temperature, becomes comparable to or even more important than heat conduction. However, an effective thermal conductivity encompassing both heat transfer modes is often used at high temperatures, due to the lack of a convenient methodology to separate the contributions from conduction and radiation, especially for high temperature thermal measurement using the prevailing instrument called the laser flash analyzer (LFA). In particular, the characteristic length scale of radiation heat transfer is often elusive. In the second part of this dissertation, a transient coupled conduction/radiation model, with the realistic boundary conditions used in the LFA, is developed to study the transient heat transfer in high temperature materials. By identifying the propagation length of photons in different portions of the spectrum, heat transfer due to photons with direct transmission and diffusive transport is delineated. In the conductive thermal conductivity of semi-transparent materials obtained from the LFA, conventional models would still cause non-negligible error at high temperatures, while the coupled model developed here can accurately quantify the radiative contribution.