Obviously there are many articles on the internet about how to reindex Magento from the CLI or Terminal. But, this is my quick reference for which indexes need to be updated based on what admin action you take.
Updating Magento Category Related Indexes
php public_html/shell/indexer.php –reindex catalog_url,catalog_product_flat,catalog_category_flat,catalogsearch_fulltext,catalog_category_product
notice the key here is not to included spaces between the comma separated values.