Google is delaying its mobile-first mandate for search indexing by 6 months in order accommodate webmasters working on other priorities during the coronavirus pandemic. Sites that have not been optimized for browsing on phones and tablets should be revamped by March 2021 lest Google's smartphone bots not include them in results.
The company has also taken this opportunity to highlight several issues it has come across with updated sites such as lowering the interaction bar to load assets, robots meta tags, viewport lazy-loading, and content blocking due to discrepancies with mobile and desktop hosts. You can take a look at the most common issues in the Google Webmaster Central Blog.
Mobile-first indexing is already active on Google's most-crawled and newly-tracked sites.