In every case, the funds use financial derivatives to accomplish what Joe Kennedy did when he borrowed other people's stock and sold it, expecting to replace it later on the cheap. But since today's funds don't actually sell stock short -- they buy contracts that accomplish this synthetically -- they are legal in accounts that don't allow short sales, including pension accounts.
The funds are designed to work with absolute precision on a daily basis, and they generally do. Over time they can wander, however. This can be due to simple tracking error -- the inability of a fund manager to do his job perfectly -- and to the different ways negative and positive numbers compound; $100 becomes $110 when it goes up 10%, but it then falls to $99 if it goes down 10%.
In the table below you'll see that, at least over a couple of months, the funds tend to deliver roughly what they promise. But they're not infallible. ProShares UltraShort MSCI Emerging Markets and Direxion Emerging Markets Bear 3X Shares are up an almost identical 19% this year, though the former is leveraged two times and the latter three times.