Reverse recovery time in rectifying diodes is a parameter that we used to be able to ignore. When the incoming AC power was 60 Hz and the current draw was a few Amps, reverse recovery time of microseconds didn't matter much. Now, we have switch-mode power supplies. Switching frequencies are in the hundreds of kHz to several MHz, and current draw is tens or hundreds of amps. Under these conditions, we ignore this spec at our own peril.
For this discussion, "current flow" means conventional current flow, not electron flow. Electron flow is in the opposite direction. In a perfect diode, when forward biased, current flows from anode to cathode. At the instant that the polarity reverses, current flow ceases. In the real world, a finite amount of time passes while the holes and electrons near the P and N material boundary combine. This amount of time is the reverse recovery time (or the transient reverse recovery time). So while holes and electrons are moving in the opposite direction from their normal conduction direction, the diode is passing current in the reverse direction. Not what you expect from your diodes.
What are the consequences? Lower power supply efficiency, of course, as we are wasting energy. And excessive heating in the diode (that's where the wasted energy manifests). Lower reliability in the diodes as the PN junction slowly deteriorates. And increased EMI due to the short high-current burst in the wrong direction. When reverse recovery time is causing EMI, it is often overlooked as the likely source and can be difficult to track down.
To fix this, you could lower your switching frequency, but then your transformers (in a flyback design) or inductors (in a buck design) get bigger. That uses up more space on the PC board and probably increases overall cost.
You can add a series R-C snubber across each diode. This will slow down the di/dt and protect the diodes. But you will get a certain amount of power dissipation in the resistor in the R-C snubber. No free lunch here.
There are variations on the R-C snubber that add an extra diode. That can help reduce the reverse current with less power dissipation (search for "RCD clamp"). Related to the transformer based designs, reduce the leakage inductance and you can reduce the reverse current problem somewhat. For example, if the transformer secondary is centered-tapped, using a bifilar winding technique can help. Better (faster) diodes will help although they will probably cost more.
These ideas can be expanded upon and I'll prepare a larger article on the topic later. For now, comments welcome.