my flight started on July 17th and was delayed for 3 hours due to some problem with flight Tyre in Bombay and i thought i will miss my connecting flight however to my surprise DELTA halted connecting flight for 2 hours in Amsterdam because there was many connecting passenger in my flight.
so yes they do hold flights in case your flight is delayed and there are many other people for same connection. During the trip I also learned if you mis your connecting flight due to flight delays they will automatically book you in next connecting flight though it may be long route, for example my connecting flight to vegas was canceled on memphis airport so they rebooked me for next day and put me in holiday express motel with 2 x $6 meal vouchers which i did not use!. However, they sent me to Detroit and then to Vegas. My one checked in bag was with them whole time but they managed to deliver it to me on vegas airport properly.
I changed my meal to hindu veg while going to usa and veg meal was good. I had same veg meal in return.