ClickHouse, an analytical columnar database, differs from PostgreSQL, a transactional OLTP database, in data modeling. When replicating data from PostgreSQL to ClickHouse, users may encounter challenges such as handling duplicates and choosing the right ordering key for query performance. To model their data efficiently in ClickHouse, users can use techniques like ReplacingMergeTree table engine, FINAL clause, argMax function, window functions, views, nullable columns, and materialized views. Choosing the right ordering key is crucial for query performance, as it acts as an index when querying data. Users can also handle DELETEs by creating row-level policies in ClickHouse based on the _peerdb_is_deleted column. By understanding these concepts and techniques, users can maximize the benefits of using ClickHouse for their analytical workloads.