Ultrasonication-mediated liquid-phase exfoliation has emerged as an efficient method for producing large quantities of two-dimensional materials such as graphene, boron nitride, and transition metal dichalcogenides. This thesis explores the use of this process to produce a new class of boron-rich, two-dimensional materials, namely metal diborides, and investigate their properties using bulk and nanoscale characterization methods. Metal diborides are a class of structurally related materials that contain hexagonal sheets of boron separated by metal atoms with applications in superconductivity, composites, ultra-high temperature ceramics and catalysis. To demonstrate the utility of these materials, chromium diboride was incorporated in polyvinyl alcohol as a structural reinforcing agent. These composites not only showed mechanical strength greater than the polymer itself, but also demonstrated superior reinforcing capability to previously well-known two-dimensional materials. Understanding their dispersion behavior and identifying a range of efficient dispersing solvents is an important step in identifying the most effective processing methods for the metal diborides. This was accomplished by subjecting metal diborides to ultrasonication in more than thirty different organic solvents and calculating their surface energy and Hansen solubility parameters. This thesis also explores the production and covalent modification of pristine, unlithiated molybdenum disulfide using ultrasonication-mediated exfoliation and subsequent diazonium functionalization. This approach allows a variety of functional groups to be tethered on the surface of molybdenum disulfide while preserving its semiconducting properties. The diazonium chemistry is further exploited to attach fluorescent proteins on its surface making it amenable to future biological applications. Furthermore, a general approach for delivery of anticancer drugs using pristine two-dimensional materials is also detailed here. This can be achieved by using two-dimensional materials dispersed in a non-ionic and biocompatible polymer, as nanocarriers for delivering the anticancer drug doxorubicin. The potency of this supramolecular assembly for certain types of cancer cell lines can be improved by using folic-acid-conjugated polymer as a dispersing agent due to strong binding between folic acid present on the nanocarriers and folate receptors expressed on the cells. These results show that ultrasonication-mediated liquid-phase exfoliation is an effective method for facilitating the production and diverse application of pristine two-dimensional metal diborides and transition metal dichalcogenides.