Last several decades have sparked a tremendous interest in mechanical properties of low dimensional systems specifically 1D and 2D nanomaterials, in large, due to their remarkable behavior and potential to possess unique and customizable physical properties, which have encouraged the fabrication of new structures to be tuned and utilized for targeted applications. In this critical review we discuss examples that represent evolution of the mechanical characterization techniques developed for 1D and 2D nanomaterials, with special emphasis on specimen fabrication and manipulation, and the different strategies, tools and metrologies, employed for precise positioning and accurate measurements of materials’ strength, elastic modulus, fracture toughness as well as analysis of failure modes. We focus separately on techniques for the mechanical characterization of 1D and 2D nanomaterials and categorize those methods into top-down and bottom-up approaches. Finally, we discuss advantages and some drawbacks in most common methodologies used for 1D and 2D specimen testing and outline future possibilities and potential paths that could boost the development of more universal approaches for technologically viable solutions which would allow for more streamlined and standardized mechanical testing protocols to be developed and implemented.