Time series data are increasingly prevalent across domains such as finance, healthcare, manufacturing, and IoT, making accurate forecasting and anomaly detection critical for decision-making and system reliability. Traditional statistical methods (e.g., ARIMA, Holt-Winters) often fail to capture complex temporal dependencies and high-dimensional interactions inherent in modern time series. Recent advances in artificial intelligence particularly deep learning architectures such as recurrent neural networks (RNNs), convolutional neural networks (CNNs), temporal convolutional networks (TCNs), graph neural networks (GNNs) and Transformers have demonstrated marked improvements in modeling both univariate and multivariate series, as well as in detecting anomalies that deviate from learned norms (Darban, Webb, Pan, Aggarwal, & Salehi, 2022; Chiranjeevi, Ramya, Balaji, Shashank, & Reddy, 2024) [1,2]. Moreover, ensemble techniques and hybrid signal-processing + deep-learning pipelines show enhanced sensitivity and adaptability in real-world anomaly detection scenarios (Iqbal, Amin, Alsubaei, & Alzahrani, 2024) [3]. In this work, we provide a unified survey and comparative analysis of AI-driven time series forecasting and anomaly detection methods, highlight key industrial application domains, evaluate performance trade-offs (e.g., accuracy vs. latency, supervised vs. unsupervised learning), and discuss emerging challenges including interpretability, data drift, real-time deployment on edge devices, and integration of causal reasoning. Our findings suggest that while AI approaches significantly outperform classical techniques in many settings, careful consideration of data characteristics, evaluation metrics and deployment environment remains essential for effective adoption.