Timescale compression offers a more modern and effective solution to data compression in PostgreSQL, outperforming TOAST by up to 10x in reducing storage size and improving query performance. Timescale's columnar compression works by consolidating multiple records into a single row with an array-like structure, followed by compression algorithms tailored to each column based on their data types. The compression process can be fine-tuned through parameters such as `compress_orderby` and `compress_segmentby`, which allow users to organize data effectively and group similar values together for better compression outcomes. By leveraging these best practices and implementing Timescale compression, users can significantly reduce the size of their PostgreSQL databases and improve query performance, making it an ideal solution for modern applications struggling with storage demands.