You can see who clicked links on the Engagement tab of any of your sent marketing messages. Your overall click rate at the top has a link below it (the "4 clicks" in the example screenshot below). This will take you to a list of the individual contacts who clicked the links in your message.

You can also access the same information on the Recipients tab by filtering for the contacts who clicked the message.

You can see the specific links each individual clicked on their timelines (and how many times and when they clicked each link).

Wondering which links are the most popular? Scroll down on the Engagement tab to see click tracking for every link in your message.

Nutshell detects internal clicks automatically and removes them from reporting (so your clicks don't skew your numbers and all click tracking is coming from external email recipients). To see link click tracking reports, send your marketing message to your audience.