Internet-based services have seen remarkable success, generating vast amounts of monitored key performance indicators (KPIs) as univariate or multivariate time series. Monitoring and analyzing these time series are crucial for researchers, service operators, and on-call engineers to detect outliers or anomalies indicating service failures or significant events. Numerous advanced anomaly detection methods have emerged to address availability and performance issues. This review offers a comprehensive overview of time series anomaly detection in Artificial Intelligence for IT operations (AIOps), which uses AI capabilities to automate and optimize operational workflows. Additionally, it explores future directions for real-world and next-generation time-series anomaly detection based on recent advancements.