Down pillows don't often wash well. You can get them dry cleaned, but most (or all?) dry cleaning chemicals are very toxic, so personally, I would toss them and buy new.
As for synthetic pillows, I wash them all the time (every few months) but the trick is to put a clean tennis ball or two in the dryer with them. It fluffs them up and helps them dry thoroughly. Yes, sometimes I need to run the dryer twice or once on a sensor setting and once on a timer setting (say an extra 50 minutes), but sometimes they dry in the first run.
I personally wash them with warm water and dry them on high heat, to kill as much as possible.
It helps to put double pillowcases on pillows, btw, when you use them, so they stay fresher, too.
You can also spray pillows with 100% white vinegar in a spray bottle and let them air dry to kill dust mites and deodorize. The vinegar smell goes away. I do that with our mattresses, too.