The complexity of monitoring cloud environments and the lack of standards so far urge for a careful analysis, systematizing and understanding of key points involved when assessing the services provided. In this context, this paper proposes a layered model for Cloud Services monitoring, identifying the multiple dimensions of monitoring, while combining the perspectives of service providers and customers. This process involves the identification of relevant parameters and metrics for each monitoring dimension, focusing on monitoring of resources, quality of service, security and service contracts. Taking a stratified view of the problem, this study contributes to achieve a clearer and more efficient approach to cloud services monitoring.