When items are dropped on top of a hopper, the hopper just leaves them there and doesn't pick them up. Also if a chest with items in it is on top the hopper, it won't pull the items from that chest. The hopper is completly empty. There is no redstone signal going into the hopper. I have tested this in creative and survival. Please look at the screen shots. I have found that when there is a chest on top the hopper, if I give the hopper a redstone signal then turn off the signal, it will pull all the items from the chest but if I put more in the chest after that it won't take them.
rplatham edit: Hoppers may work when at least 1 item is already in the hopper. See
MCPE-13087. I'm resolving all other build 4 "hoppers don't work" tickets as duplicates of this one. P.S. Good job on the ticket Jason.
_rplatham edit: Put a hopper funneling into anything(like a chest or something) then fill up the hopper and notice only items in the first slot get funneled into the chest or whatever you have it funneling into.
_rplatham edit: Hoppers may be pushing items only into dispencers, etc. that are below the hopper, not beside it.