Red meat does require some ageing in a chilled storage area in order to let enzymes rather than putrification tenderise the meat and develop flavour (but not make it gamey).
Beef sold in most supermarkets is far too fresh and consequently often tough and tasteless. Beef needs to be hung for at least 3 weeks and better if it is 4 or 5 weeks old. There is a good reason for supermarkets selling it too fresh, if you think about the amount of "money" hanging in cold stores for the extra few weeks you can see why they'd want to get it on the shelves.
The best meat to buy is from a local butcher who will tend to hang it longer but if you are in your supermarket look for the beef on the "bargain shelf" as it will be the oldest in the shop, if it is dark rather than bright red and well marbled, that's the one to buy. You can test tenderness by poking it, tender meat will be softer to the touch. If it resists the touch then leave it on the shelf.
Venison also needs a short hanging period, maybe up to a week in a chilled area, but I usually eat it fresher than beef, about the same as lamb.