Network Traffic Monitoring and Analysis (NTMA) represents a key component for network management, especially to guarantee the correct operation of large-scale networks such as the Internet. As the complexity of Internet services and the volume of traffic continue to increase, it becomes difficult to design scalable NTMA applications. Applications such as traffic classification and policing require real-time and scalable approaches. Anomaly detection and security mechanisms require to quickly identify and react to unpredictable events while processing millions of heterogeneous events. At last, the system has to collect, store, and process massive sets of historical data for post-mortem analysis. Those are precisely the challenges faced by general big data approaches: Volume, Velocity, Variety, and Veracity. This survey brings together NTMA and big data. We catalog previous work on NTMA that adopt big data approaches to understand to what extent the potential of big data is being explored in NTMA. This survey mainly focuses on approaches and technologies to manage the big NTMA data, additionally briefly discussing big data analytics (e.g., machine learning) for the sake of NTMA. Finally, we provide guidelines for future work, discussing lessons learned, and research directions.