Check logs, limits and reports
See if the crawler has added content to the search index, and if your users are finding what they're looking for in SharePoint Online.
View search usage reports
This article describes how you can use search reports in the SharePoint admin center to find answers to questions about how search is being used in your organization. You can for example see the number of queries and the top queries. Learn more.
In SharePoint Online, you can't turn query throttling on or off, but you can use client-type information to make sure lower-priority clients like automated queries don't squeeze out higher-priority clients like UI. Learn more.
Set crawl log permissions
Use the crawl log to see if crawled content was successfully added to the search index, if it was excluded because of a crawl rule, or if indexing failed because of an error. Learn more.
Look up the limits to SharePoint Online search. For example, there are limits to the number of entries you can have in a custom search dictionary and the number of results that can be returned for a query. Learn more.