Engineering-scale problems generally can be described by partial differential equations (PDEs) or ordinary differential equations (ODEs). Analytical, semi-analytical and numerical analysis are commonly used for deriving the solutions of such PDEs/ODEs. Recently, a novel physics-informed neural network (PINN) solver has emerged as a promising alternative to solve PDEs/ODEs. PINN resembles a mesh-free method which leverages the strong non-linear ability of the deep learning algorithms (e.g. neural networks) to automatically search for the correct spatial-temporal responses constrained by embedded PDEs/ODEs. This study comprehensively reviews the current state of PINN including its principles for the forward and inverse problems, baseline algorithms for PINN, enhanced PINN variants combined with special sampling strategies and loss functions. PINN shows an easier modelling process and superior feasibility for inverse problems compared to conventional numerical methods. Meanwhile, the limitations and challenges of applications of current PINN solvers to constitutive modelling and multi-scale/phase problems are also discussed in terms of convergence ability and computational costs. PINN has exhibited its huge potential in geoengineering and brings a revolutionary way for numerous domain problems.