Obviously you are speaking about manual transmissions here. Upon downshifting to the next lower gear, blip the throttle to bring the revs up just before you release the clutch. With practice this will become second nature and allow you have the smoothest/jerk free downshifts the car is capable of. What you are doing is bringing the engine rpm up to where the next lower drive ratio will take it to. Practice. practice, practice. When the revs don't match, releasing the clutch creates slip if you let it out slowly - this wears the clutch plate. If you let the clutch out fast, you get a jerk feeling. You can't do this when upshifting because the rpm's drop with the selection of the next higher gear. Something you might try to get an idea of what is happening is (going at slow speeds), put the shifter in neutral, then apply slight pressure on the stick towards the next lower gear while blipping the throttle slightly - all the time NOT using the clutch. You will feel the synchronizers mesh and the next lower gear will slip right in. Just be careful when and if you do this - but it does work.