Only twice in my life have I had anything close to a religious epiphany: 1) the first time I tried psychedelics, and 2) the time I finally 'got' UML: I was faced with an enormously complex software project that was far beyond my level of experience and skill set, and I didn't have the faintest clue where to start... it was the sort of project that makes you feel slightly terrified and incompetent. After several false starts, I realised I needed to try a different approach, so out of desperation I dug up an old college textbook on systems analysis and tried to design the entire system on paper away from the computer. I started with a use case diagram, then numerous class diagrams, then sequence diagrams, then activity diagrams. In a matter of hours, I'd nailed the ENTIRE project, without straining my brain the slightest. I was ecstatic! It felt like I'd just acquired a superhuman power or a secret black art -- I'd transcended the capabilities of mere mortals, into the realm of gods! In that moment, I saw the essence of UML, and it was power! As nerdy as it sounds, it was certainly one of the most profound and memorable experience I've had -- taking something I knew moderately well (UML), and seeing an aspect of it that I could never have anticipated, and using it to solve a problem that was completely beyond me.
Saying all that, I should qualify that I'm not a UML fundamentalist, nor do I think everything should be modelled. People often criticise over-abstraction and "architecture astronauts", and rightfully so. There is an inherent danger to modelling, but if you're an experienced coder (and more importantly the person who's going to be implementing the designs, so as to stay grounded and realistic) then there's immense power in abstracting away the code and the limitations that come with "thinking in code". Under the right conditions, modelling enables you to see the essence of the problem and derive a well-structured solution. That, at least, is my opinion.
...and on the topic of Agile doing away with the need for modelling: the whole point of modelling is to enable fast iterations. It's amazing how fast ideas can develop with just a whiteboard and some thinking space. Why waste time coding?