While I've never done it, I'm told you can put your meat on a rack in the refrigerator for a few days and effect a type of "aging".
I wouldn't age filet mignon, but would stick with steaks (t-bone, porterhouse, etc.)
In the old days, beef was pasture fed until about 2 years of age. Then they were brought into the barn for the last, oh, 60 days, and fed corn, beet pulp, oats, etc. Then they were taken to the meat locker where they were butchered and hung up to "dry age". Dry aging took place in a controlled environment and the meat was open to the air. Mold usually grew and would be cut off before packaging for the consumer.
Nowadays, they use a process called "wet aging" in which the beef is wrapped in a sort of saran wrap, to retain moisture. Moisture equals weight equals more money $$.
There are now places that sell "dry aged" beef. They're worth looking for, but because dry aging loses moisture, the beef is priced higher.
Have never to this day tasted beef like the '50's and '60's down in Iowa though! Most beef these days is farmlot beef which is constrained, fed lo-grade antibiotics, hormones, etc. Most ruminants are treated in this manner these days. They even have put ground glass in the feed so the animal's stomach bleeds and it gets more protein in its diet. I've even heard of them putting ground up cardboard in the feed.
But the above is the way they used to do it!