How can I view the Git history in Visual Studio Code?

I recommend you this repository, https://github.com/DonJayamanne/gitHistoryVSCode

Git History

It does exactly what you need and has these features:

• View the details of a commit, such as author name, email, date, committer name, email, date and comments.
• View a previous copy of the file or compare it against the localworkspace version or a previous version.
• View the changes to the active line in the editor (Git Blame).
• Configure the information displayed in the list
• Use keyboard shortcuts to view history of a file or line
• View the Git log (along with details of a commit, such as author name, email, comments and file changes).

GitLens has a nice Git history browser. Install GitLens from the extensions marketplace, and then run "Show GitLens Explorer" from the command palette.

You won't need a plugin to see commit history with Visual Studio Code 1.42 or more.

Timeline view

In this milestone, we've made progress on the new Timeline view, and have an early preview to share.
This is a unified view for visualizing time-series events (e.g. commits, saves, test runs, etc.) for a resource (file, folder, etc.).

To enable the Timeline view, you must be using the Insiders Edition (VSCode 1.44 March 2020) and then add the following setting:

"timeline.showView": true