In the 50's and 60's there were plenty of people hunting and killing deer with 35-40 lb bows. A kid's bow of mine that drew 32# at 24" took a doe a couple years ago. I chewed the guy's butt about it because 1) I gave it to his kid, not him 2) He had the ability and the resources for a bow of better hunting quality. He just wanted to see if he could kill a deer with it. He was lucky, in my estimation, and got a clean kill. If you don't KNOW FOR STONE COLD CERTAIN that the bow is up to the job, don't even think of using it.
When confound, ooops, typo, compound bows came out the rage for 60-70-80 lb recurve bows exploded on the scene. Most states have confusing requirements, some claim draw weight is all you need, others go to kinetic energy, still others require a certain grain weight arrow fly a certain distance (trying to imagine a Conservation Officer upholding that law - talk about needlessly complicated).
I think the best rule of thumb is a minimum of 40# draw weight and shooting at least 10 grains per lb of draw weight, and non-mechanical broadheads so sharp that you often wake up in the middle of the night with screaming terrors of them slicing through everything in sight.