I liked their storyline, but I didn't get the point, when they started to be attracted to each other.

It seems to me that it was a platonic love for most of the time. Perhaps they loved each other deeper than that but just never understood that until later.

I think it was more of a "we love each other, but won't act on it unless we absolutely have too in case it ruins our friendship and makes one of us have to resign" thing.

With all due respect to the OP, I would like to disagree with him or her. It is my ascertation that it was actually Mrs. Hughes that fell in love first. I firmly believe that she turned Joe Burns down, not because of her devotion to Downton, but her devotion to Mr. Carson. Yes, it took me a while to join Team Chelsie, but her actions during the first episodes of season 4 sealed the deal for me. Then, I started watching the earlier episodes again and could almost see her heart breaking when he was talking about going to Haxby. She looked like she was on the verge of tears when she told him she would miss him. Then, there was every time he got sick and she would just hover over him.

Mr. Carson, however, I don’t think he realized his feelings for her until that famous day at the beach. Remember, it was her that had to prod him into it.

(Note: this debate is waaaay better than Mary vs. Edith)