The exponential growth of mobile applications and services during the last years has challenged the existing network infrastructures. Consequently, the arrival of multiple management solutions to cope with this explosion along the end-to-end network chain has increased the complexity in the coordinated orchestration of different segments composing the whole infrastructure. The Zero-touch Network and Service Management (ZSM) concept has recently emerged to automatically orchestrate and manage network resources while assuring the Quality of Experience (QoE) demanded by users. Machine Learning (ML) is one of the key enabling technologies that many ZSM frameworks are adopting to bring intelligent decision making to the network management system. This paper presents a comprehensive survey of the state-of-the-art application of ML-based techniques to improve ZSM performance. To this end, the main related standardization activities and the aligned international projects and research efforts are deeply examined. From this dissection, the skyrocketing growth of the ZSM paradigm can be observed. Concretely, different standardization bodies have already designed reference architectures to set the foundations of novel automatic network management functions and resource orchestration. Aligned with these advances, diverse ML techniques are being currently exploited to build further ZSM developments in different aspects, including multi-tenancy management, traffic monitoring, and architecture coordination, among others. However, different challenges, such as the complexity, scalability, and security of ML mechanisms, are also identified, and future research guidelines are provided to accomplish a firm development of the ZSM ecosystem.