The increasing reliance on real-time analytics and sensor-driven systems has elevated the importance of maintaining high data quality in streaming environments. This literature review provides an overview of data quality (DQ) concepts, representations, and processing techniques tailored to continuous data streams. It traces the evolution of data quality from early database systems to modern big data and streaming contexts, emphasizing intrinsic, representational, and contextual quality dimensions such as accuracy, completeness, consistency, and timeliness. The paper reviews major DQ models, metrics, and standards, highlighting methods for assessing and improving quality in sensor-based and high-velocity data systems. Furthermore, it examines state-of-the-art data cleaning, fault detection, and anomaly management approaches, identifying their limitations in flexibility and generalizability. As a literature review, it synthesizes key foundational and recent contributions rather than providing an exhaustive systematic survey. The literature was analyzed through targeted review of seminal and recent works focusing on peer-reviewed contributions to DQ models, metrics, and processing techniques. Finally, the study discusses emerging trends such as adaptive, pattern-based, and AI-driven quality processing toward building accessible, real-time, and domain-independent frameworks for quality-aware data stream management.