Dye sublimation is interesting.

Once again, you use an inkjet printer, with specially formulated inks.

You print your design onto a paper, and then transfer the image onto your substrate (whatever it may be), by vapourising the ink so that it infuses into whatever it is that you are printing. That is the simple explanation.

Not all materials can be used for dye sublimation. They do need a particular coating to accept the ink. Polyester shirts work well, straight off the rack, but better if they are white, because the inks are not opaque, so whatever colour is underneath it, will affect the final colour. Your fishing shirts are done this way.

We use this process to print coffee mugs, key rings, coasters, bar mats (there is a size limit here), mouse pads, drink coolers, photo panels etc.