To enhance the energy conversion efficiency between heat and electricity, the thermal conduction of materials needs to be suppressed, and the microscopic mechanisms must be better understood. Thermal conduction in solids is closely related to lattice vibration, which is conventionally characterized by phonon propagation; however, diffuson-like thermal transport can become predominant in materials with ultralow thermal conductivity. New strategies for a simultaneous suppression of both propagative and diffusive thermal transports will be discussed in this talk. Zintl compounds were recently found to exhibit exceptional thermal energy conversion efficiency. The electrical and thermal transports and the carrier properties of Zintl compounds will be presented. It will be shown that a high thermoelectric figure of merit over a broad temperature range can be realized through the suppression of the carrier excitation.