Nephrolithiasis (kidney stone disease) is a common urological disease that has a high clinical and economic impact. The early diagnosis is needed to avoid complications like obstruction of the ureter, infection, impaired kidney functioning. Traditional imaging modalities, such as ultrasonography, kidney-ureter-bladder radiography, and non-contrast computed tomography, are common but have a number of limitations, specifically their operator dependence, radiation, and low sensitivity to small or radiolucent stones. This review follows a PRISMA-based methodology to conduct a systematic review of studies published between 2015 and 2025 on the topic of computational intelligence methods such as artificial intelligence, machine learning, and deep learning to detect kidney stones based on medical images. Major scientific databases were considered in studies according to imaging modality, preprocessing method, model architecture and performance measures. Deep learning models, especially, Convolutional Neural Networks and U-Net-based frameworks, are highly effective in detection and segmentation tasks and have been reported to have accuracy of 86 to 99.9 percent, Dice coefficients over 0.85 and AUC of up to 0.99 in controlled data. Hybridization to combine ML classifiers, including Support Vector Machines, further improves the performance of classification. Yet, these outcomes are commonly limited through small datasets, class imbalance, external validation, and overfitting, which have an impact on real-life generalization. The use of computational intelligence has greatly improved the detection of kidney stones by enhancing automation, precision, and reproducibility. However, there are still major issues, such as the standardization of the dataset, interpretability of the models, and limitations to the clinical implementation. Explainable AI, federated learning, and 3D volumetric analysis should be prioritized in future research to create diagnostic systems.