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This thesis explores the utilisation of underdense regions of the Cosmic Web as a tool for studying cosmology. Underdensities, known as cosmic voids, provide a complementary approach for understanding the large-scale structure of our Universe, as well as providing a unique environment to explore the effects of dark energy. An application of the spherical model to void evolution is presented, showcasing its ability to provide non-linear density and velocity profiles for voids. This methodology is then applied in order to reconstruct the initial conditions of the void using a late-time void density profile. Using this reconstruction, the spherical model yields non-linear late-time velocity profiles which are used to predict redshift-space distortions around voids, showing the capacity to constrain cosmological parameters using measurements in the non-linear regime. Furthermore, this thesis investigates how cosmologists can utilise the advances of weak gravitational lensing to exploit the underdensities of the Universe. A study of the weak lensing measurement around voids is presented with a focus on the SLICS simulation suite and the KiDS and GAMA surveys. A watershed void finding algorithm, zobov, is applied to both the simulations and data, showing that the geometry of the GAMA survey does not lend well to extracting a weak lensing signal from voids due to limitations from both the survey volume and geometry. In contrast, projected underdensities, known as troughs, and the full, projected density spectrum, known as Density Split Statistics, are both shown to yield great potential as cosmological tools. The final chapter of this thesis investigates the use of this novel approach to explore non-ΛCDM cosmologies using the cosmo-SLICS simulations, showing how underdensities can potentially constrain the equation-of-state of dark energy with a higher precision than overdense regions. Chapter 1 of this thesis provides a brief overview of cosmology, while Chapter 2 introduces the theory of weak gravitational lensing. Chapter 3 discusses the spherical model applied to void evolution and redshift-space distortions around voids, while Chapter 4 explores the weak gravitational lensing signal around voids in simulations and data. Chapter 5 utilises a suite of simulations to investigate the sensitivity of Density Split Statistics to dark energy models.