Emerging novel properties of nanomaterials have been attracting attention. Besides quantum electronic transport properties, the breakdown of classical Fourier’s law and other significant quantum thermal behaviors such as quantized thermal conductance, phonon subbands, size effects, the bottleneck effect, and even interaction between heat and spin degrees of freedom have also been revealed over the past two decades. These phenomena can be well captured by the nonequilibrium Green’s function (NEGF) method, which is pretty simple under ballistic or quasi-ballistic regimes. In this review, we mainly focus on two aspects: quantum phonon transport and thermal-spin transport in low-dimensional nanostructures. First, we present a brief history of researches on thermal transport in nanostructures, summarize basic characteristics of quantum thermal transport, and then describe the basic algorithm and framework of the phonon NEGF method. Compared with other methods, the NEGF method facilitates numerical calculations and can systematically incorporate quantum many-body effects. We further demonstrate the power of phonon NEGF method by recent research progress: from the phonon NEGF method, distinct behaviors of phonon transport compared with those of electrons, intrinsic anisotropy of phonon transport, radial strain within elastic regime as quantum perturbation, two kinds of interfacial transport behaviors, defect-induced localization of local phonon density of states, unobservable phonon localization, etc, have been discovered in some particular low-dimensional nanomaterials or nanostructures. Second, the new concept of “spin caloritronics”, which is devoted to the study of thermally induced spin-related transport in magnetic systems and offers a brand-new way to realize thermal-spin or thermoelectric energy conversion, is also introduced. After concisely discussing the spin Seebeck effect, spin-dependent Seebeck effect, and magneto-Seebeck effect, we present the linear response theory with spin degree of freedom and show that by combining with linear response theory, NEGF method is also applicable for studying spin caloritronics, especially spin thermoelectrics. Finally, recent research on quantum dot models or numerical calculation of real materials give hints to the searching for high-ZT materials. With the ever-increasing demand for energy and increasing power density in highly integrated circuits, quantum thermal transport properties are not only of fundamental interest, but also crucial for future developing electronic devices. Relevant researches also pave the way to spin thermoelectrics, which has vast potential in thermoelectric spintronic devices and energy harvesting.