I got an especially good question to “Ask Petzal,” inquiring whether accuracy improves if you let a rifle barrel “age”–i.e., don’t clean it for a while and let the funk accumulate. My brief answer was no*, probably the opposite will happen; clean the damn thing every 20 shots or so.

I think I’ve seen more mythology accumulate around barrels than any other facet of rifle shooting. Here are some of the things I think are facts:
All other things being equal, short, fat barrels shoot better than long thin ones or short thin ones.
Muzzle brakes do seem to make barrels more accurate. The Browning B.O.S.S. system which is a barrel weight, definitely works.

Barrels of average quality–factory tubes and low-priced aftermarket barrels–do seem to improve somewhat after they have 100 or so rounds through them, assuming they’re properly cleaned. I think repeated firing knocks some of the rough edges off the rifling.

Fine barrels–Schneider, Lilja, Pac-Nor, Shilen, Jarrett–are so good when they reach your rifle that they are accurate from the get-go. They will not improve.
Rough-bored barrels can shoot extremely well. The most recent example of this was the Remington Model 783 I tested, whose button-rifled barrel was a true inanimate hideosity that had more annular rings than a redwood tree, but which shot sub-MOA with distressing regularity.

Probably the best barrels are cut-rifled or button-rifled, but I have seen some rotten examples of both, and some excellent hammer-forged barrels, which is supposed to be the cheap way of doing it.

How the muzzle is crowned does not make any difference as long as it’s clean and square to the axis of the bore.

The best barrels are stainless steel because top-grade stainless blanks are “cleaner” (fewer inclusions) than chrome moly, and top barrel makers prefer to work with them. Also, stainless bores last longer.

There is no single “correct” method for cleaning a barrel. Use a good rod(s) and keep it (them) clean.

There are all sorts of fads for “accurizing” barrels. Moly is one. Freezing is another. Ignore them. If you have a good barrel don’t mess with it.

There probably are “black-hole” barrels, mystical tubes that will shoot anything with spectacular accuracy. There’s probably more than the barrel involved, but so be it.

*Although I know one F-class shooter who can put ten bullets in a teacup at 600 yards who swears that his groups improve if the bore has 75 or 80 rounds through it with no cleaning, and who am I to argue?