I really enjoying working on novelty books for small children, there are lots of different types: Touch and Feel, with different fabrics and textures, Lift-the-Flap, with hidden images,  Pull-and-Slide, with parts that move, etc. 
Lots of care and attention goes into the design and engineering of these books. The illustrator has to provide artwork for the flaps and moving parts and the backs of the extra pieces too, so sometimes there can be twice as much artwork as in a regular book.
Here's an example of one I illustrated for Scholastic: Alfie's Amazing Farm, The flaps had die cut holes, which 'revealed' something underneath - but when you opened the flap, it was something else entirely.
The little boy Alfie walks around the farm expecting to see ponies, chickens etc, but sees much more unusual animals - lots of fun for me to illustrate! The original artwork was painted in Winsor and Newton gouache on smooth white card, and there is another book in the series  Millie's Amazing Garden which features a little girl in her garden, who encounters some hidden exotic animals as she goes about her day.