Physics-informed neural networks (PINNs) solve differential equations by approximating the solution with a neural network and minimizing the corresponding residual. Due to the popularity of PINNs, a multitude of extensions and variations has been proposed. This chapter explores advanced methodologies and extensions of PINNs, such as the deep energy method, variational approaches, and improved boundary condition handling. These techniques are demonstrated through basic one-dimensional and two-dimensional examples using static bars and plates. Furthermore, the connection to the finite element method is established, showcasing the similarities and limitations of physics-informed neural networks.