This review discusses recent advances and future research priorities in the transition-metal dichalcogenide (TMD) field. While the community has witnessed tremendous advances through research conducted on two-dimensional (2D) TMD crystals, it is vital to seek new research opportunities beyond developed areas. To this end, in this review we focus principally on articulating areas of need in the preparation and analysis of TMD crystals encompassing dimensionalities and morphologies beyond 2D. Ultimately, the development of new synthetic methods to control key structural features of low-dimensional TMD crystals (e.g., dimensionality, morphology, and phase) will afford access to a broader range of breakthrough properties for this intriguing material class. We begin with a brief overview of the evolution of 2D TMD research, discussing both the synthetic methods that have enabled the preparation of these materials and the manifold properties they possess. We focus the bulk of our review on discussion of recent advances associated with 1D TMD crystals, which are often referred to as TMD nanoribbons, and include a discussion of recent efforts in 0D systems. We discuss synthetic strategies that have been developed to prepare such beyond 2D crystals and highlight their unique physical and chemical properties. After reviewing the host of analytical tools available for characterization of TMD materials, we identify future analytical instrumentation needs. We conclude with a discussion of the prospects of beyond 2D TMD crystals in optoelectronics, catalysis, and quantum information science.