A very salient moment of surprise was when I realized that my mental model of a simple three-quark proton was deeply (or simply) wrong:
You may have heard that a proton is made from three quarks. Indeed here are several pages that say so. This is a lie — a white lie, but a big one. In fact there are zillions of gluons, antiquarks, and quarks in a proton. The standard shorthand, “the proton is made from two up quarks and one down quark”, is really a statement that the proton has two more up quarks than up antiquarks, and one more down quark than down antiquarks. To make the glib shorthand correct you need to add the phrase “plus zillions of gluons and zillions of quark-antiquark pairs.” Without this phrase, one’s view of the proton is so simplistic that it is not possible to understand the LHC at all.
http://profmattstrassler.com/articles-and-posts/largehadroncolliderfaq/whats-a-proton-anyway/
What still surprises me, whenever I think of it, is how we live in a such a big world, even on the smallest scales we are able to probe. And also that things like nuclei happen to be stable over long enough timescales for things like chemistry and life to occur.
All of those gluons and quark-antiquark pairs are every bit as stable as the Earth's gravitational field. They're elements of the ground state for a quark.
The process of finding the ground state for a particle from its interactions, including dragging in virtual pairs to screen high field intensities around the singularity, is called Renormalization.
I recently flipped through the "Cartoon Guide to Physics", expecting an easy-to-understand rehash of ideas I was long familiar with; and that's what I got - right up to the last few pages, where I was presented with a fairly fundamental concept that's been absent from the popular science media I've enjoyed over the years. (Specifically, that the uncertainty principle, when expressed as linking energy and time, explains what electromagnetic fields actually /are/, as the propensity for virtual photons of various strengths to happen.) I find myself happy to try to integrate this new understanding - and at least mildly disturbed that I'd been missing it for so long, and with an increased curiosity about how I might find any other such gaps in my understanding of how the universe works.
So: what's the biggest, or most surprising, or most interesting concept /you/ have learned of, after you'd already gotten a handle on the basics?