Graphyne (GY) and graphdiyne (GDY) have properties including unique sp- and sp2-hybrid carbon atomic structures, natural non-zero band gaps, and highly conjugated π electrons. GY and GDY have good application prospects in many fields, including catalysis, solar cells, sensors, and modulators. Under the influence of the boundary effect and quantum size effect, quasi-one-dimensional graphyne nanoribbons (GYNRs) and graphdiyne nanoribbons (GDYNRs) show novel physical properties. The various structures available give GYNRs and GDYNRs greater band structure and electronic properties, and their excellent physical and chemical properties differ from those of two-dimensional GY and GDY. However, the development of GYNRs and GDYNRs still faces problems, including issues with accurate synthesis, advanced structural characterization, the structure-performance correlation of materials, and potential applications. In this review, the structures and physical properties of quasi-one-dimensional GYNRs and GDYNRs are reviewed, their advantages and disadvantages are summarized, and their potential applications are highlighted. This review provides a meaningful basis and research foundation for the design and development of high-performance materials and devices based on GYNRs and GDYNRs in the field of energy.