I started out with a piece of fabric all ironed out flat, then using wonder-under I added the hearts and the bias tape was also iron on. Everything got ironed on in place before I started to sew but after I sewed all the things down it puckers all over the place.
What did I not do right? This is a first time applique for me so any ideas will certainly be welcome.

I am wondering when you sandwich it and pull it taunt before you quilt it, if the wrinkles will come out.

the hearts look fine. i'm wondering if you stretched the bias tape when applying it... that is where it is puckered. if you quilt the spaces a little on the heavy side, it will draw up the puckery space and that may solve the problem

If the applique was stiff and the block background was lite weight it is hard to get it to stitch down evenly. In the past I have put a sheet of paper behind my background when stitching down something that has been fused. Tear the paper away when done. Helps keep everything smooth.

Deb's idea may work, give it a try.:)

did you use the right tension for the thickness of the bias tape? It looks like it might have stretched..in the end, it might block out. Try getting lightly damp and pulling it out and pinning it down...might need a large piece of cardboard covered in wax paper for this...then spray starch it and let it dry...then remove carefully and iron good....

I may just try that and then try another one with out the bias tape to see how that comes out to.

I would have used a walking foot to sew the bias tape down. I agree with Nancy it appears that the puckering is in the bias tape, NOT the hearts. and DO NOT pull it through the machine, only guide the fabric from the font. This is something I had a hard time learning! :)

The bias has stretched. It could be that the bias tape stretched or the bias of the fabric under it stretched. I have found it is always tricky to sew a long bias seam.

Did you sew it using a stabilizer behind? If you didn't that's why it puckers. When you do machine applique you need to stabilize the fabric and I find that starching the fabric is not enough.

The word is "taut". Taunt means to mock or jeer.