IBM has successfully run a globally distributed Apache Cassandra cluster on Kubernetes in the cloud. The company faced challenges such as global replication, scaling out and in, operational tasks, and monitoring while moving from a simple Apache Cassandra deployment to a global distribution that's operationally viable. To address these issues, they created a Kubernetes service for each Cassandra node and assigned each a private IP address. They also used Helm to automate their deployments. The process involved fine-tuning and creating a deployment in Kubernetes with every Cassandra volume and backup volume attached to it for maintenance and backups.