Atomically thin two-dimensional (2D) materials have flourished as one of the leading topics in condensed matter physics and materials science for nearly two decades. From carbon-based graphene, the family of 2D materials now includes hundreds of compounds spanning a diverse array of chemical elements and potential applications. Patterning low-dimensional nanostructures in these emerging materials constitutes a viable method of precisely engineering their fundamental properties but has yet to be fully realized experimentally. In this thesis, we present a variety of techniques for tuning the chemical, mechanical, optical, and electronic characteristics of 2D materials via the controlled fabrication of nanostructures. A brief introduction on confined nanoscale geometries and the development of 2D materials beyond graphene is first provided. We then describe methods utilized in this work for the scalable synthesis, clean processing, and high-resolution characterization of various atomically thin compounds. In phosphorene, we report the formation of low-dimensional architectures through electron beam lithography and nanosculpting as well as techniques for inhibiting systemic oxidation. The resulting few-nm-wide 1D nanoribbons and 2D antidot lattices exhibit quantum confinement effects that yield tunable electronic and phononic properties. We subsequently show the creation of 0D pores and 2D porous membranes in molybdenum and tungsten disulfide through novel processes such as focused ion beam irradiation, laser-induced photo-oxidation, selected area electron exposure, and acid etching. Nanofluidic measurements, optical spectroscopy, and atomic resolution electron microscopy are used to explore structural, optoelectronic, and ionic transport phenomena. Lastly, we present approaches for patterning van der Waals superlattices and developing electron microscope field-effect transistors. The research described here paves the way for future studies on the nanoscale engineering of 2D materials beyond graphene.