Disclaimer: I possibly don't know what I am talking about as I don't really know Instagram mechanics at all, but I am guessing they are similar to Facebook's.
Also if you view the activity feed (in a different corner of the app) you can see what your friends have been up to. This is where you will see more explicitly "Sally, Sue, John and Dave liked a post by Mr. Famous" (and similar activity).
Wrong.
In your notifications screen (who liked your stuff), you can change pane and instead see what your friends has liked.
Most people don’t know it, but yes, it means you can “spy” on your spouse or vica-verce.
It’s the sort of creepy most people wanted to avoid when they left Facebook, and unknown to them, Instagram still has it.
My comment was merely meant as a correction to an incorrect claim and making people aware that they can be spied upon, also on Instagram.