Computer imaging techniques are crucial in fields like medicine and engineering, where CT scans help diagnose patients, and non-destructive testing (NDT) ensures the safety of structures such as airplane wings. In this thesis, we study the full waveform inversion (FWI) problem from a deep learning point of view. FWI, initially developed in seismology and applied recently in NDT, is explored using various neural network architectures, namely convolutional and feed-forward neural networks. Our initial goal was to apply a feed-forward neural network (FNN), along with the "Sample Where It Matters" (SWIM) weight sampling algorithm, to solve the FWI problem outlined in \cite{main}. We wanted to propose a new method for the research described in the cited article. The approach sought to reduce the number of trainable parameters and hence inference time by fixing hidden layer weights and only optimizing the output layer. However, our FNN failed to predict the objective material distribution, even after adjusting and testing out different initializations designed to make the algorithm converge easier, using different SWIM domain approximations. A supervised learning experiment confirmed the network could not approximate the discontinuous ground truth gamma using gradient descent, which explained the failure in solving the FWI problem. Seeking to determine the capabilities of neural networks to solve the FWI problem, we tested smoother ground truth functions: (i) a Gaussian and (ii) a sinusoidal function. In addition, we have also studied the effect of simulating a larger domain. Convolutional neural networks (CNNs) could solve both supervised learning and FWI tasks, independent of the discretization and domain size, whereas FNNs failed. With an extended domain and the same number of grid points as in the original experiments, an FNN with four hidden layers and 500 neurons per layer successfully handled smooth functions in the supervised learning framework, successfully solved the FWI problem for the sinusoidal-shaped function, however struggled with the Gaussian function in FWI. Lastly, we compared two CNN initializations for FWI on smooth functions: (i) Xavier-Glorot and (ii) weights trained on a void-less domain. We found that the first worked better for the Gaussian function, while the second was more effective for the sinusoidal function. In this thesis, we also discuss improvements and future work that could help answer our study's unresolved questions.