How to update apps in iTunes 11.3? I'm on OS X 10.9.4, with iTunes 11.3.1.  I got a new phone and am trying to get it set up on a new mac. Previous to this, I already sync'd the phone to an older mac (to get all my old apps and data from the backup), which my previous phone was sync'd to. That appeared to go fine.

Now I'm trying to sync the phone to a newer mac, because the old one is very slow. When I tried to sync, I got the message that 'this phone is already sync'd on another computer, do you want to erase and sync from this one?" I said yes. It appeared to sync.  But I know I need several updates, and I can't figure out where to do that.

When I look at the Apps tab in iTunes, with the phone selected, it displays the apps on a list on the left, and the home screens on the right. The only button next to each app is 'Remove'.
This is for iTunes 11.4, but I think it's the same in 11.3 and other versions around here, for anyone looking.

I had this issue too, because there isn't enough space on my iDevices to update in place.

Open iTunes, make sure you're in "Library" and not the Store.  At the top left there's a drop down menu, it defaults to "Music".  Use it to select "Apps".  Then in the top center area below the status box that shows sync progress and the like is "Updates".  Click that, then "Update All Apps" in the bottom right of the window.

Presto, utilizing your computer's network connection and hard drive for better app updating.