In recent years, the increasingly precise constraints on the value of the Hubble constant, H0, have highlighted a discrepancy between the results arising from early-time and late-time measurements. A potential solution to this so-called Hubble tension is the hypothesis that we reside in a cosmic void, i.e. an underdense cosmic neighbourhood characterized by a faster local expansion rate. In this thesis, we model this scenario through the Lemaître-Tolman-Bondi formalism for an isotropic but inhomogeneous universe containing matter, curvature and a cosmological constant, which we denote by ΛLTB. We numerically implement this framework with two different formulations for the local matter density profile, respectively based upon a more realistic Gaussian ansatz and the idealized scenario of the so-called Oppenheimer-Snyder model. We then constrain the background cosmology and the void parameters involved in each case through a Markov Chain Monte Carlo analysis with a combination of recent data sets: the Pantheon Sample of type Ia supernovae, a collection of baryon acoustic oscillations data points from different galaxy surveys and the distance priors extracted from the latest Planck data release. For both models, the resulting bounds on the investigated parameter space suggest a preference for a -13% density drop with a size of approximately 300 Mpc, interestingly matching the prediction for the so-called KBC void already identified on the basis of independent analyses using galaxy distributions. We quantify the level of improvement on the Hubble tension by analyzing the ΛLTB constraints on the B-band absolute magnitude of the supernovae, which provides the calibration for the local measurements of H0. Since no significant difference is observed with respect to an analogous fit performed with the standard ΛCDM model, we conclude that the potential presence of a local void does not resolve the tension.