Graphdiyne has a unique pi-conjugated structure, perfect pore distribution and adjustable electronic properties of sp2, sp hybrid planar framework. Due to the presence of acetylenic bonds, it has more excellent properties compared to grapheme, such as a unique structure-dependent Dirac cone, abundant carbon bonds and a large bandgap. As one of the important raw materials for nanodevices, it is extremely important to study the thermal properties of graphdiyne nanoribbon. This paper mainly introduces and discusses recent academic research and patents on the preparation methods and thermal conductivity of graphdiyne nanoribbons. Besides, the applications in engineering and vacancy defects in the preparation process of graphdiyne are described. Firstly, taking thermal conductivity as an index, the thermal conductivity of graphdiyne with various vacancy defects is discussed from the aspects of length, defect location and defect type. In addition, the graphdiyne nanoribbons were laterally compared with the thermal conductivity of the graphene nanoribbons. The thermal conductivity of graphdiyne with defects increases with the length and width, which is lower than the intrinsic graphdiyne. The thermal conductivity of the acetylene chain lacking one carbon atom is higher than the one lacking the benzene ring. Typically, the thermal conductivity is larger in armchair than that of zigzag in the same size. Moreover the thermal conductivity of nanoribbons with double vacancy defects is lower than those nanoribbons with single vacancy defects, which can also decrease with the increase of temperature and the number of acetylene chains. The thermal conductivity is not sensitive to shear strain. Due to the unique structure and electronic characteristics, graphdiyne has provoked an extensive research interest in the field of nanoscience. Graphdiyne is considered as one of the most promising materials of next-generation electronic devices.