This work investigates the potential of neural networks in the processing of artificial intelligence, especially in smart systems, and explores their applications regarding advancing automation, user experience, and resource management. The methodology will include collecting data from public datasets and international organizations, preprocessing or cleaning, normalization and augmentation of data, followed by the development of different neural network models: Convolutional Neural Networks for image recognition; Recurrent Neural Networks and Long Short-Term Memory for speech recognition and time series prediction; hybrids for such complicated tasks as energy consumption forecasting andhealth data analysis. Results are very high for a wide variety of datasets, with CNNs attaining state-of-the-art in image recognition, LSTMs doing the same in speech recognition with very low word error rates, and the hybrids quite effective in predictive analytics and health data analysis. The discussion has been about how neural networks are impacting smart systems in a big way while also presenting the challenges regarding the requirements around data and computational resources and model interpretability. Future directions in this regard may include transfer learning, explainable AI, edge computing, and quantum computing to further enhance neural network capabilities.