The recent development of smart devices has lead to an explosion in data generation and heterogeneity. Hence, current networks should evolve to become more intelligent, efficient, and most importantly, scalable in order to deal with the evolution of network traffic. In recent years, network softwarization has drawn significant attention from both industry and academia, as it is essential for the flexible control of networks. At the same time, machine learning (ML) and especially deep learning (DL) methods have also been deployed to solve complex problems without explicit programming. These methods can model and learn network traffic behavior using training data/environments. The research community has advocated the application of ML/DL in softwarized environments for network traffic management, including traffic classification, prediction, and anomaly detection. In this paper, we survey the state of the art on these topics. We start by presenting a comprehensive background beginning from conventional ML algorithms and DL and follow this with a focus on different dimensionality reduction techniques. Afterward, we present the study of ML/DL applications in sofwarized environments. Finally, we highlight the issues and challenges that should be considered.