Cross-posting for Dan Harrington and his Office 365 Term-of-the-Day blog.
The low-level details of crawling and indexing are not obviously available in a SharePoint Online site, but can be exposed via an eDiscovery Center site. The procedure detailed below describes how this information can be made accessible to a SharePoint administrator.
In SharePoint Online in an Office 365 Enterprise environment there is no direct administrative control over the configuration of crawling and indexing. Unlike an on-premises SharePoint 2013 farm, there is neither visible Search Service Application (SSA), no Content Sources to configure, nor any crawl rules to test and deploy. Despite these differences the content of an SPO tenant does get crawled and indexed, often becoming searchable within an hour of being added to a site.