Hi and welcome, EPM! Your new garden might have a lot of established clumps of perennial plants that have been hiding underground until spring warmth wakes them up. They're not necessarily spreading or being invasive, let's hope!
I'm not sure what that lovely plant is, in your picture above, but if you could please fill in your profile with your location we'll have a much easier time identifying your plants. The little blue person in the upper right corner is where your profile is. We need more than just a zone, your city/state/country will give us climatic conditions.