According to "The NIST Definition of Cloud Computing," in IaaS, "the capability provided to the consumer is to provision processing, storage, networks, and other fundamental computing resources where the consumer is able to deploy and run arbitrary software, which can include OSs and applications. The consumer does not manage or control the underlying cloud infrastructure but has control over OSs, storage, and deployed applications; and possibly limited control of select networking components (e.g, host firewalls)."

Network, CPU and Disk(storage) are key subsystems in cloud environment that should be monitored.

The primary tool of governance is the contract between a cloud provider and a cloud customer (this is true for public and private cloud). The contract is your only guarantee of any level of service or commitment Ref: CSA Security Guidance V4.0

With compliance inheritance, the cloud provider's infrastructure is out of scope fora customer's compliance audit, but everything the customer configures and builds on top of the certified services is still within scope.
Reference: CSA Security GuidelinesV.4 (reproduced here for the educational purpose)