Elasticsearch memory management involves understanding resource allocation, particularly Java heap memory, to prevent performance issues such as circuit breaker exceptions and unassigned shards. As Elasticsearch is a Java application, it requires careful monitoring and configuration of heap memory, which should be up to half of the system's physical RAM. Troubleshooting common issues like configuration errors, high request loads, and unbalanced shard allocation can often be resolved by adjusting JVM heap settings, optimizing queries, or scaling resources. The article emphasizes the importance of understanding heap sizing, allocation health, and circuit breaker mechanisms to maintain optimal Elasticsearch performance. It also highlights the support systems and resources available, like documentation, community forums, and training, to assist users in managing these challenges effectively.