Cloud storage services like AWS S3 provide scalable and durable storage in the cloud. Files and objects can be stored in S3 buckets and accessed from anywhere with an internet connection. S3 offers different storage classes like Standard and Glacier that provide varying levels of availability and durability depending on how often the data needs to be accessed. Other AWS storage options include EBS for raw block-level storage attached to EC2 instances, EFS for shared file storage across EC2 instances, and Glacier for long-term archival storage of non-critical data.