With the developments of the electronics and energy technologies, studies on nanostructure engineering of the emerging thermoelectric materials and thermal logic devices are drawing increasing attentions. In this review, we focus on several promising thermoelectric materials, and study the mechanisms of thermal transport engineering in the atomic and nano-scale structures theoretically and experimentally, with a micro-nano scale thermal transport measurement system developed by our research group. Such research focuses include: the atomic alloying of Si1-xGex alloy films with full components, the mismatched interfaces of Bi2Ca2Co2Oy layered-structure single crystals, the ionic localized resonances of superionic conductor A0.5RhO2 (A=K, Rb, Cs) single crystals, and the loose microstructures in quasi-one-dimensional ZrTe5/HfTe5 single crystals as well as the SnSe2 intercalations in SnSe single crystals. The influences of various scale structures and interatomic forces on the thermal transport properties are summarized, offering effective engineering strategies on developing potential thermoelectric materials with low thermal conductivity and excellent thermoelectric performance. Besides, the realization of effective dynamic engineering of thermal conductivity using phase transition, along with its potential applications in thermal logic devices are introduced.