Over the last decades, deep learning models have rapidly gained popularity for their ability to achieve state-of-the-art performances in different inference settings. Deep neural networks have been applied to an increasing number of problems spanning different domains of application. Novel applications define a new set of requirements that transcend accurate predictions and depend on uncertainty measures. The aims of this study are to implement Bayesian neural networks and use the corresponding uncertainty estimates to perform predictions and dataset analysis. After an introduction to the concepts behind the Bayesian framework we study variational inference and investigate its advantages and limitations in approximating the posterior distribution of the weights of neural networks.