Excitons are one of the most important fundamental quasi-particles, and are involved in a variety of processes forming the basis of a wide range of opto-electronic and photonic devices based on II-VI semiconductor nanowires and nanobelts, such as light-emitting diodes, photovoltaic cells, photodetectors and nanolasers. A clear understanding of their properties and unveiling the potential engineering for excitons is of particular importance for the design and optimization of nanoscale opto-electronic and photonic devices. Herein, we present a comprehensive review on discussing the fundamental behaviours of the excitons in one-dimensional (1D) II-VI semiconductor nanomaterials (nanowires and nanobelts). We will start with a focus on the unique properties (origin, generation, etc) and dynamics of excitons and exciton complexes in the II-VI semiconductor nanowires and nanobelts. Then we move to the recent progress on the excitonic response in 1D nanomaterials and focus on the tailoring and engineering of excitonic properties through rational controlling of the physical parameters and conditions, intrinsically and extrinsically. These include (1) exciton-exciton interaction, which is important for 1D nanomaterial nanolasing; (2) exciton-phonon interaction, which has interesting applications for laser cooling; and (3) exciton-plasmon interaction, which is the cornerstone towards the realization of plasmonic lasers. The potential of electric field, morphology and size control for excitonic properties is also discussed. Unveiling and controlling excitonic properties in II-VI semiconductor nanowires and nanobelts would promote the development of 1D nanoscience and nanotechnology.