When you work out, are you supposed to feel the muscles as you work them?

Ok, so over the years I guess I went from being real lazy to a little more active and one thing I've noticed is that when I work out (working on toning my legs at the moment) I feel the pain of the muscles being toned and worked. Its not just in the moment as Im working them, but they can hurt for days. Is that supposed to happen? Thanks.
When you work out, are you supposed to feel the muscles as you work them?
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