I have played around with it a little bit. (I don't own a tenkara rod, so I used a cheap graphite pole as a substitute.) Despite my poor equipment, I did catch fish.
The rods are specially designed to cast just a mono leader, so I think they'd be pretty fun for playing fish.
There's a ton of info here:
Tenkara Rods, Lines and Flies
... and here:
Tenkara Fishing