Synergies between neural networks and traditional surrogate modelling techniques have emerged as the forefront of data-driven engineering. Neural network-based surrogate models, trained on carefully selected experimental data or high-fidelity simulations, can predict behaviours of complex systems with remarkable speed and accuracy. This review examines the current state and recent developments in neural surrogate technologies, highlighting their expanding roles in engineering design optimisation and generation. It also covers various feature engineering methods for representing 3D geometries, the principles of neural surrogate modelling, and the potential of emerging AI-driven design tools. While feature engineering remains a challenge, especially in parameterising complex designs for machine learning, recent advancements in code/language-based representations offer promising solutions for digitalising various design scenarios. Moreover, the emergence of AI-driven design tools, including text-to-CAD models powered by large language models, enables engineers to rapidly generate and evaluate innovative design concepts. Neural surrogate modelling has the potential to transform engineering workflows. Continued research into geometric feature engineering, along with the integration of AI-driven design tools, will speed up the use of neural surrogate models in engineering designs.