Where does the fat go?

So, I was thinking about all the fat on our bodies that has been going away.  So, where does it go?

I've always heard conflicting answers.  Does fat turn to muscle?That seems impossible to me.  The body, I've  heard has a certain number of fat cells.  I've heard they shrink when you lose weight.

So what is happening?  If the cells are shrinking then what was in them and where did it go?  Does it come out when you sweat or go to the bathroom? 

This question is more amazing to me the more pounds someone loses.  Because when you see someone down over 100 lbs from before you ask yourself where it all went.

I don't eat a lot of meat, mostly because I just don't really like it that much.  I really should start, because I don't get anywhere near enough iron, but that’s another day's problem.  As far as protein goes, I was surprised when I started monitoring my protein intake how much protein can come from dairy products (which I love)! 

For example, 1 cup of the skim milk I drink, has 9 grams of protein, half a cup of my 1% cottage cheese has 16 grams, and a 100 g tub of Source yogurt (one of those little single sized containers) has 4 grams protein.  That’s a total of  29 grams just for eating these in a day, which I never miss! Also, my cereal of choice (Allbran) has 4 grams for a 1/2 a cup, putting my up to 33 grams for the day.  Then from getting 1 gram or so here and there from fruits and veggies, it puts me up to 38 grams before I even eat supper, which is when I tend to get my usually small meat portion.  At 50% of my body weight, I should be having 65 grams of protein in a day.  So I may have to make sure I have a good source at supper, but as long as you are careful, its defiantly achievable.