Non-planar architectures of the traditionally flat 2D materials are emerging as an intriguing paradigm to realize nascent properties within the family of transition metal dichalcogenides (TMDs). These non-planar forms encompass a diversity of curvatures, morphologies, and overall 3D architectures that exhibit unusual characteristics across the hierarchy of length-scales. Topology offers an integrated and unified approach to describe, harness, and eventually tailor non-planar architectures through both local and higher order geometry. Topological design of layered materials intrinsically invokes elements highly relevant to property manipulation in TMDs, such as the origin of strain and its accommodation by defects and interfaces, which have broad implications for improved material design. In this review, we discuss the importance and impact of geometry on the structure and properties of TMDs. We present a generalized geometric framework to classify and relate the diversity of possible non-planar TMD forms. We then examine the nature of curvature in the emerging core-shell architecture, which has attracted high interest due to its versatility and design potential. We consider the local structure of curved TMDs, including defect formation, strain, and crystal growth dynamics, and factors affecting the morphology of core-shell structures, such as synthesis conditions and substrate morphology. We conclude by discussing unique aspects of TMD architectures that can be leveraged to engineer targeted, exotic properties and detail how advanced characterization tools enable detection of these features. Varying the topology of nanomaterials has long served as a potent methodology to engineer unusual and exotic properties, and the time is ripe to apply topological design principles to TMDs to drive future nanotechnology innovation.