Aha.. I found some pics of a Peter's Honey.. BINGO!  those leaves DO look like mine!   Now, If I could only dry some of them for making Italian Fig cookies..  

you are not italian at all are you, LOL

...This is my way of saying "you are soooo Italian" ;)

I always knew of wasps being great for the garden and for stinging people. I got curious after reading this trail and did my research.  I still think the wasps are not attacking the fruits, but the little insects that destroy the fruits (fruit fly, gnats, moths, fruit worms,  etc) 
see the article.

http://www.motherearthnews.com/organic-gardening/benefits-of-wasps-yellow-jackets-zw0z1303zkin.aspx#axzz35p88VTx2

Yeap, Grasa!
Those yellow wasps were eating my fig wasps by a truckload every day. It is good I have a few caprifigs nearby and there were enough for everybody. 
But I can tell you, that was a massacre to watch!

Bees, wasps, and hornets all seem to enjoy eating figs, and can create a dangerous situation for those allergic to stings. Around here at least, they are definatly eating figs. You have to make sure there are none on a fig when you pick them. Keeping the figs picked helps, they seem to be worse on figs that are very ripe. I think I will have to try some traps this year. We have yellow jackets that nest in the ground, usually discovered after going over them with a lawn mower. They are the most aggressive I have seen around here. One nest last year was removed by some animal, probably skunks, as we see them in the yard digging for food.

Mike in Hanover, VA

For me, luckily they would only stick to a couple figs at a time and there would be up to 10 on one fig so I left them to their figs and ate mine, not a significant loss for me, later in the season when the cold nights came in, the figs got less tasty on the tree they went after so I let them have their fill, some figs just dried on the tree and they would slowly pick at them.  They seem to only go after 1 tree for me and left the rest alone.

Last year I lost a lot of figs to yellow jackets. I used a trap to catch some and a shop vac with some soapy water in the canister. I used a skinny piece of pipe attached to the hose so that I only got the yellow jackets and not the fig. The figs that they started to eat were left on the tree as bait to keep them from starting on a new fig. Then when they began eating I'd suck em up in the vac and they would drown in the canister. Just make sure you have a wet and dry vac before you try this. It didn't eliminate all of them but it really cut down on their population.

Why are some of you referring to them as bees? Yellow Jackets are wasps, are they not? Guess if they're munching away at your prize fruit, you're not gonna be too bothered about their Linnean classification, right?

Anyroad, I can add my personal experience, for what it's worth. Whenever we arrived late season (end Aug/early Sept) for our hols in Greece, most of the figs on our Gk Yellow had extensive wasp/hornet damage, and harvesting any undamaged was always a case of risking a possible sting or two. How I escaped getting stung is still a mystery to me. 

Meanwhile, back home in the UK, I noticed insect damage on our ripe BT's (ID'd on this forum as a Gene Vashon) for the first time last year, then one day saw a wasp crawling out of a whole in one of the figs. There was no way I was gonna let them have free range on my figs, so I deployed the only solution that I knew about - bag each one of them as they 'turned'.

And yes, it worked. If I had hundreds ripening all at once, then ok, I might think again. But as there were never more than around a doz. at any one time, it was a manageable task. And glad I took the trouble - they were quite yummy.

Yellow Jackets destroyed my grapes all the time.  I never got any.  I put organza bags on all of my figs and the YJs went from bag to bag and never found their way in.  I'll shoot some video this year.  When I had grapes I'd have hundreds of them and they even built a nest in the ground.  With the organza bags I'd see 1 or 2.  I'd rather bag than spray.  For those of you with too many figs to individually bag consider frost or insect cloth around each tree or an enclosure like TucsonKen built.  It cuts sunlight by about 30% but it's better than having swarms of YJ.

Grasa, you're right about everything else, but YJ devour fruit.  At the end of the article it mentions that they love to eat fruit.  They talk about discarded pieces but they'll tear into fruit on the vine or tree just as much.  They are the bane of peach orchards especially.  They are not fit to live.

These work good too. They also keep out fruit flys and imgagine they would work for sour beetles. No tying involved, just cover and wrap the end around itself.

ok.. let's just call them fig eating monsters for fun.  I would love to have bagged them but I'm serious, My tree was covered by hundreds of them. There was a huge hive of them somewhere around here.  We live near a golf course.   I'm thinking of a smoke machine...lol

Bee activity greatly decreases at night time. But, if you think they all fly back to where they came from you'll be in for a surprise. I do a great deal of gardening at night with my headlamp on, it is not uncommon to find bees and yellow jackets just hanging out on a leave waiting for the sun. At least they aren't flying around, I think if you put on a headlamp and wear leather gloves you could probably pick your figs a lot more comfortly.