Artificial neural networks have been widely applied in reservoir engineering. As a powerful tool, it changes the way to find solutions in reservoir simulation profoundly. Deep learning networks exhibit robust learning capabilities, enabling them not only to detect patterns in data, but also uncover underlying physical principles, incorporate prior knowledge of physics, and solve complex partial differential equations. This work presents the latest research advancements in the field of petroleum reservoir engineering, covering three key research directions based on artificial neural networks: data-driven methods, physics driven artificial neural network partial differential equation solver, and data and physics jointly driven methods. In addition, a wide range of neural network architectures are reviewed, including fully connected neural networks, convolutional neural networks, recurrent neural networks, and so on. The basic principles of these methods and their limitations in practical applications are also outlined. The future trends of artificial intelligence methods for oil and gas reservoir development are further discussed. The large language models are the most advanced neural networks so far, it is expected to be applied in reservoir simulation to predict the development performance.