Neural network models in simple terms are nothing but mathematical functions of the inputs. Unlike functions represented by Fourier, wavelet or any other basis function, the parameters (coefficients) of the neural networks correspond to basis functions defined primarily by a stack of linear operations and activation functions. Thus, these parameters are evaluated through an optimization problem, and neural network models have proven to be good universal function approximators, granted the functions are continuous, like those describing wavefields, including our data. I will share examples of neural network functions that help us solve some of the outstanding challenges we face in waveform inversion. These include NN misfit functions, measuring the distance between the observed and synthetic data in a way that are trained to allow us to avoid cycle skipping. It also includes an NN wavefield functional solution to the wave equation that can also fit the data. The key feature of NN functions is their flexibility as they are optimized to implement specific tasks, and in our case these tasks are directed to support waveform inversion.