From what I can tell, you're looking in the correct place:

https://www.strava.com/challenges

Scroll through the Recommended For You, or filter based on activity type. For the ones you've joined, the button says Challenge Joined instead of Join Challenge. 

A very simple solution to make this more user-friendly in your case would be for Strava to add "Active Challenges" to the existing filters. Then you could simply click that filter to see all the ones you've already joined. (You might consider adding this idea to the Feature Suggestions forum, or if you have a better idea... )

@kevinpeters Group Challenges can only be created and viewed on mobile. You can read more about them here.

We are in 2024 and still no way to see it on the website, just mobile app?

Yes, this is annoying.  The inconsistency between the website and the app is staggering.  

Also, most Strava challenges are not much of a challenge for people pushing themselves.  For example, in April for "walk" and "hike", the "hardest" one is 18ish miles (30 km).  I had to create a custom one because we are doing 90 miles rucking in April (don't get me started on Strava's inability to create a "ruck" category) but I can't interact with it on a computer, which I'd prefer to do when doing group updates.