I've been washing my fabrics only if it's going to be used as a quilt for a bed or snuggling in; not just for display on a wall.
But, I forgot about batting... should I be washing that too? If so, any advice about drying, ironing, anything?

I use warm and natural cotton batting - and I machine wash and dry it.
If removed promptly, it smooths out very nicely.

I would do nothing with polyester batting except let if fluff up a bit.

simply answer - no

I use warm and natural or warm and white. In the early days, that brand had oily nibblets in it that required washing. Since then, the process has been refined and it is not necessary to prewash. If it's wrinkled and won't hang out, I throw it in the dryer with a damp towel.

My main reason for not prewashing is the effect of the shrinkage on the finished quilt.

.....but as with so many quilty things, it is personal preference.

I don't

I guess the main thing is to have an idea of what the batting will do, and then go for the look that you want to achieve.

I like my quilts to be flat, flat, flat and still be approximately the same size after they are washed.

Most battings come with instructions on whether and how to pre wash and dry. A cotton batting will shrink more than a polyester one, and if you don't pre wash will give you that old fashioned look. I guess it just depends on what look you want. I am not aware of any disadvantage to not pre washing. I am usually so excited to get my top sandwiched that I forget to even think about pre washing! I have heard people say that you can just spray it good with water and iron with a hot iron and that will take care of some shrinkage, but I have never tried this!

I don't either

Polyester doesn't shrink so there's no reason to prewash it. Besides, it would shred if not yet quilted.

For cotton batting, it depends on the type of batting and the look you want. Cotton batting with a needle-punched scrim, such as Warm 'n' Natural, will hold together for washing if you want absolutely no shrinkage at all. It doesn't shrink much anyway, though.

A cotton batting without needle-punched scrim must be handled very carefully to avoid shredding. Fairfield cotton batting benefits from pre-washing if you want to hand quilt it because it has a coating on each side. This coating works well for machine quilting but can make hand needling more difficult. To get rid of the coating you soak the batting in the washing machine and spin it out; no agitation cycle at all unless you want shredded batting! Most other cotton battings do not benefit from pre-washing and the batting cover instructions usually indicate they should not be prewashed.

I personally don't prewash any type of batting. The only reason I can think to do so would be if I developed an allergic reaction to the chemicals used to process a batting.

I soak my cotton batting in the washer, spin it out and throw it in the dryer. I do not wash it, I just soak it for about 20 minutes.

Mary