When SharePoint 2013 got released there was something missing in the UI. There was no breadcrumb control anymore like in SharePoint 2010. A couple of clients and users were struggling finding their way on the site. In March 2013, I created a script that allowed you to transform the SharePoint text in the suite bar (on the left side) into a breadcrumb.
Info: read more about it - Transform the "SharePoint" Suite Bar Text into a Breadcrumb with PowerShell.
The downside was that this script only worked for on-premises environments because this functionality was not available on SharePoint Online.
Now with the new era of SharePoint development with SharePoint Framework and the extensions, we have a way to re-introduce the breadcrumb control again.
Info: be aware that the SharePoint Framework extensions are currently in developer preview.
One of the available extensions is the application customizer. This one allows developers to add scripts / HTML to specifically provided placeholders. Like for example a header and footer placeholder. By making use of this extension model and the header placeholder, I created a breadcrumb sample project which is available in the SharePoint sp-dev-fx-extensions GitHub repository.
Info: check out the sample here - https://github.com/SharePoint/sp-dev-fx-extensions/tree/master/samples/react-application-breadcrumb
Here is another screenshot of the breadcrumb output:
Feel free to contribute and make it better.