Large-scale software systems are currently designed as distributed entities and deployed in cloud data centers. To overcome the limitations inherent to this type of deployment, applications are increasingly being supplemented with components instantiated closer to the edges of networks—a paradigm known as edge computing. The problem of how to efficiently orchestrate combined edge-cloud applications is, however, incompletely understood, and a wide range of techniques for resource and application management are currently in use. This article investigates the problem of reliable resource provisioning in joint edge-cloud environments, and surveys technologies, mechanisms, and methods that can be used to improve the reliability of distributed applications in diverse and heterogeneous network environments. Due to the complexity of the problem, special emphasis is placed on solutions to the characterization, management, and control of complex distributed applications using machine learning approaches. The survey is structured around a decomposition of the reliable resource provisioning problem into three categories of techniques: workload characterization and prediction, component placement and system consolidation, and application elasticity and remediation. Survey results are presented along with a problem-oriented discussion of the state-of-the-art. A summary of identified challenges and an outline of future research directions are presented to conclude the article.