Changing climates exacerbate the difficulties facing water management, worsening droughts, floods, and water contamination. These disruptions are greater than traditional hydrological models can cope with, due to complexity and data scarcity. This paper discusses recent developments of Artificial Intelligence (AI) and Machine Learning (ML) for sustainable management of groundwater systems. We analyze prominent techniques such as Artificial Neural Networks (ANNs), Convolutional Neural Networks (CNNs), Autoregressive Integrated Moving Average (ARIMA), and Random Forests (RF) models for piezometric level forecasting, aquifer characterization, potential mapping, and groundwater quality monitoring. The findings indicate strong predictive performance, with ANNs reaching 0.99 \(R^2\) values for recharge, and more advanced models like the Outlier-Robust Extreme Learning Machine (ORELM) achieving a correlation coefficient ( \(R\) ) of 0.96 with limited input data. CNNs, achieving roughly \( 0.31\, \text {m}^2 \) Mean Square Error (MSE) in aquifer mapping and effective storage estimation, are outperformed by other models in climate extrapolation over time. RF performed better overall, achieving high Area Under Curve (AUC) values such as 0.90 for potential mapping and 0.94 in ensemble configurations, proving effective for quality assessment. Obstacles persist with interpretability and generalizability. Furthermore, the limitations of ARIMA and RF models compared to LSTM networks show the difficulty of working with sequential non-linear data. As discussed in this paper, further advances are needed in the integration of hybrid physics-AI models, Explainable AI (XAI), addressing data heterogeneity, improving data quality, ethically implementing the technology. Interdisciplinary collaboration is needed to unlock the promise of AI in adaptive groundwater management under climate uncertainties.