In the Middle Ages, in contrast, hunting was very much an activity for elites. Nobles loved to hunt, to the the point that giving up hunting was a sign of serious penance. Several saints started life as rich lords but were converted to the religious life when, on a hunting trip, they saw an animal carrying a cross.
Fantastic stories often involved hunting, such as capturing a white (albino) hart or trapping a unicorn, as seen in this late medieval tapestry.
Probably the main source of meat on a noble table was from hunting, rather then livestock raising. Nobles hunted various kinds of deer (hart, roe) and also boar, though boar were both rarer and a lot more dangerous. Hunting was both sport--competing to see who could catch the most--and a chance to show off.
Until extremely recently, England had fox hunts, where well-to-do riders and their hounds chased foxes across the countryside, leaping hedges and having a great time. This was the last vestige of the medieval style of hunting, though in the Middle Ages they preferred to hunt something worth eating.
Medieval men and women also hunted with hawks. A "mews," where the hawks were kept, was found in every castle. Training a hawk to fly off, catch a bird, and bring it back was an important and time-consuming skill. A variety of hawks went to the hunt on a rider's (gloved) fist, including goshawks, that could take a full-sized goose.
Then as now, over-hunting will reduce the game. Nobles thus did not want the peasants to hunt, though no one particularly cared if they trapped a few rabbits or caught song-birds using lime spread on twigs. Great landowners created game preserves where only they could hunt.
The New Forest in England is not actually "new," being established as a game preserve in the late eleventh century by King William II ("Rufus"). Although we think of the word 'forest' as just a place with trees, it originally meant a place set aside. The New Forest now is mostly known for its semi-wild ponies, to be feared for liking to eat an unattended picnic lunch.