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Submillimetre observations of protoplanetary discs have revealed a wide range of complex substructures in the dust continuum. Rings, gaps, and cavities, are now a common sight in many discs. In this thesis we study the dust morphology of protoplanetary discs observed with ALMA. We then model the substructure using gravitationally unstable discs, and conclude by comparing our models to actual data. We look at 794 protoplanetary discs observed with ALMA during Cycles 0–5. We find that only 56 discs show resolvable substructure; 7% of the sample. We sort the discs into four categories: Rim, Ring, Spiral, and Horseshoe, based upon the most prominent morphology seen in the dust continuum. We derive stellar ages and masses using isochrones and evolutionary tracks. We find no trends in each category relating to the stellar age or mass. We find that a rim of material is the most populous substructure seen in protoplanetary discs, followed by concentric rings of dust and gaps. A horseshoe–like concentration of material and spiral arms are rare substructures seen only in relatively old and young systems, respectively. We confirm the ubiquitous nature of rims and cavities in protoplanetary discs by showing that the majority of discs that have a rim in submillimetre emission, also features the same in scattered light. We also find that all discs classified as horseshoe show spiral arms in scattered light, indicating that the same mechanism may be responsible for the formation of these two morphologies. We find that the majority of protoplanetary discs in the ALMA Archive have been observed at resolutions insufficient to resolve substructure. For the discs observed at high resolutions of /0.1”, we find that 42% of discs show substructure. This increases to 60% for the discs observed at ‘ultra–high’ resolutions of /0.04”. Thus, the fraction of discs observed by ALMA showing substructure may increase from 7% up to 60% provided ‘ultra–high’ resolution observations are used for all observations. Smooth particle hydrodynamic simulations are used to model the substructure seen in discs of three protostars using gravitational instabilities. The initial conditions used are based upon actual ALMA observations. We are only able to create substructure in the disc of HD 36112 - where the surface density is found to be sufficiently high. Synthetic observations are run to determine the robustness of our models. We are able to recreate the spiral arm seen in the ALMA observations of HD 36112. This has not been done in previous modellings of this protostar. We find that multiple mechanisms are required in order to fully recreate all substructure components seen in the complex disc surrounding HD 36112. We show that synthetic observations are unable to resolve all of the structure present in our disc models. This results in outer disc radii being truncated, as well as an overestimation of central cavity extents. We also find that artificial substructures can be created in synthetic observations as a result of spiral arms in disc models being smeared. We thus confirm that the populous rim substructure seen in ALMA disc observations may be a resolution effect. The surface densities required to form substructure within protoplanetary discs via gravitational instabilities are much higher than is currently observed. Therefore, we are either missing a substantial fraction of disc masses when making observations, or we are missing a key aspect of physics when modelling the substructure within protoplanetary discs.