Admins can view more details on a Learner's training progress by going to their user overview page. From the Users tab of your Settings, click on the Learner's name to access the page:

You can filter the page to view the Training assignments or Events the user is registered for. The data can also be exported as a CSV.

By clicking on the Trainings box, you can search a training by title:

Using the Source option will allow you to filter the trainings by Assigned or Self-Enrolled:

Status will allow you to filter trainings by their completion status like 'In Progress' or 'Completed':