I thought about starting a thread on this too.
As I mentioned, H and I have a don't-ask-don't-tell policy.
H knows I have (had) other relationships. He knows *who* (in the sense of knowing their names, knowing a bit about them, how we met, etc.) I'm in a relationship with. My first b/f was someone he'd never met, but heard me talk about. My second b/f was someone who he knew and had met, but wasn't friends with himself (we'd been social as couples and "double dated" a couple of times both before and after M and I became intimate).
Right now I'm actively looking for another relationship. I meet people for coffee or drinks after work and H knows when I do. I tell him both becuase I want him to know what's going on in my life in that sense and for safety reasons (he knows where I'm meeting and what time and knows if he doesn't hear from me after a certain amount of time, there might be a problem). He will ask how the date went, but I don't give any more detail than "Oh, it was fine, but we didn't really click." or "He was a nice guy and I think we'll meet again." H doesn't want more detail than that, really, he just wants to know generally where things are.
When I was dating my last b/f, I would tell him "Oh I'm having lunch with M today" or "M is going to Denver in April and I think I'm going to try to go with him" or something like that. But again, other than asking "How's M doing?" he didn't want details of our relationship or our dates.
When M and I broke up, he was super sweet and comforting and gave me lots of space and time. He was willing to be a shoulder if I needed one, but honestly I needed time to hide and lick my wounds, and I was feeling awkward about accepting comfort from him in that situation.
He has no desire be involved with the people I'm involved with, although he'd like to know about them. If he were to decide to have another relationship, I think I'd feel much the same way. I would be happy, wouldn't mind meeting her, wouldn't mind having him talk about her, but don't really need details.
It really works for us, and that's the important thing.