It's much more chilled if you're an FTB, or you don't have to move in on completion date. Then you literally just wait around for a phone call. I would strongly suggest picking up the keys ASAP and going into the house to check for nasty surprises, even if you're not moving in that day - I've heard stories of gaining access to find all the lightbulbs and door handles had been taken!
If, on the other hand, you're in a chain and completing on both sale and purchase, it can be very fraught. Exhibit A - our most recent move. We completed on the sale at 10 am and moved out - only to hear from the solicitor that our purchase had stalled because the vendor (a property developer) had gone on holiday without signing a critical bit of paperwork, and unless something could be done to rectify that, we wouldn't be able to complete on the purchase that day. So we sat in the car, with all our belongings in a moving van, for 5 hours, technically homeless, wondering what the hell we were going to do, because it was the Friday before a bank holiday weekend, so if it wasn't sorted that day, it wasn't going to get sorted until the following week - and all we had with us was the kettle, some teabags and the clothes on our backs.
In the end, the estate agent managed to get the vendor on his mobile, and then with his consent the solicitors agreed that the selling solicitor could sign the paperwork on his behalf. We then got the keys, after 6 of the most stressful hours of my life.
Of course, had we failed to complete, we would have been entitled to both punitive interest payments and compensation for out of pocket expenses from the vendor - but at the time, that didn't feel like much of a silver lining!