My fly vest contains, for the full catch trout or die trying expedition:
leader wallet, containing factory tapered leaders in several sizes and lengths as well as some hand-tied leaders for special situations and two shooting heads and a sinkinking leader or two
5spools of tippet material 0X, 2X, 3X, 4X, 6Xand when latesummer flows have the streams down 7X
foam strike indicators
putty indicator
Dinsmore lead and lead-substitute split shot(I like Dinsmore because it's English and therefore classy

)
Angling Evolutions Shake-N-Float fly-dry powder/floatant and a bottle of Fly Sauce
a bottle of Gerkhe's Xink to apply to leaders
Loon Outdoors Sun Set Super Patch, a UV activated wader patch that works on wet or dry neoprene
nippers, hemostats, jig eye clearer(really helps to clean out head cement if you tie your own flies) and hook sharpener
spare reels(for my 5 wt.) or spare spools(for the 6 wt. and 8 wt.) with a wf-f, dt-f, and a sink-tip and if I'll be fishing stillwater or deep slackwater above a dam a dt full sinking line
the spare spools/reels go in the back pocket with a rain jacket and a bag of granola or trail mix and water bottle, camera
landing net is clipped to the back as well
and then there are the fly boxes


that would be a whole other topic, but generally 1 box of streamers, a Scientific Anglers System Xflybox 1 side weighted numphs-1 side unweighted nymphs and emergers, 1 box of dries(typically generic Adams, Near Nuff's, etc., 2 or 3 kinds of caddis and a stonefly or two) and a small box of wets
and after I get it all in there it only weighs 20 or 30 lbs.