In this research, different models are used to construct volatility surfaces and these models are compared with each other in terms of accuracy. The models range from the SSVI to neural networks. Specifically, we look at the SSVI, the feedforward neural network and the gated neural network. Attention is also paid to the incorporation of financial conditions in the considered models. In addition, we propose a framework which uses two neural networks in combination with the weighted mean squared error as a loss function to construct a volatility surface belonging to one trading day. We found out that this approach appears to be very accurate and outperforms all the other approaches. The thesis is structured in such a way that it starts with the construction of a volatility surface for 1 trading day, later in the research for the sake of examining the robustness of the models we used data belonging to several trading days.