The most common way to print on polyester is through dye sublimation. This means printing with disperse dyes on special paper and sublimating into the fibers using a heated calendar.
In polyester dye sublimation, dyes/inks are infused into the fibers so there is no issue with crocking (color rubbing off). The hand of the fabric will not change either.
Fabrics with at least 60% polyester can be dye sublimated, making brilliant color, a soft hand, and photographic detail possible.
Another polyester printing method is direct disperse, where coated fabric is printed on directly.