I've mercifully only had a couple of problem foxes over the years. One got ambitious enough to dig a hole under my perimeter fence way in the back, which, unfortunately for the fox, created an ideal snaring opportunity. I set one and caught him within 24 hours. They're usually pretty easy to snare, easier than trapping them, so you might want to explore that option. It's not too difficult to set up something that forces a fox to go through a small narrow space if they want to get at some tasty bait, but remember that a snare doesn't discriminate in what it catches and that a properly set one kills quickly...wouldn't count on being able to release a 'mistake', in other words...
The other fox, I knew he was around because he was coming on the property at night and it was winter, with enough snow already on the ground that I was leaving my gate open full-time. I'd find his tracks coming and going down the laneway and then all around the chicken house and runs, and--rather surprisingly--about the can corral where I store garbage. I guessed he must be a very hungry fox and set a live-trap with the usual cat food bait and got him within two days. A silver fox, as it turned out, and one which I think a fox farm might have dumped, which explained his rather stupid behaviour...they're usually more wary and difficult to live-trap, unless you get creative and use something impossible to resist, like live bait. Live-traps are always the best choice if there's ever any possibility of catching someone's pets, either your own or the neighbour's. The worst thing that happens there if you catch the wrong animal is that you sacrifice a can of bait. (Or sometimes several cans of bait, like with the little black and white cat I caught THREE TIMES one week because the particular flavour I was using must've been like crack cocaine to her or something, sheesh!)