The golden age of handhelds was a wonderful time to live in, I guess it would be like it is now with every kid having a cellphone except back then we had Tiger handhelds and some of the really cool people (me) had the watch version.
Tiger game out with a ton of handheld games which if you look at them now are not impressive in the least, but back then they were totally awesome. The standard handheld was just a simple LCD screen with a picture behind it representing whatever the game board was to be.
For instance, if the game was baseball a picture of a baseball field would be grafted onto the screen and it would never change. When you played the game tiny black icons of players and the ball would appear in specific designated areas. Sure, most of the games were simple and difficult at the same time. The lack of graphics sometimes made the games hard to play, but hey we had a video game in our hands.
What was really cool were the advance games. These handhelds (term used loosely) were much bigger and normally came in the shape of a vehicle. Some of the more famous handhelds were Afterburner and Outrun. Those games did not have graphics that were any better, but the large screen and the fact they were shaped like the cockpit of an F-16 or a race care made it much cooler.
You can still find a bunch on handhelds on sites like Amazon or check out the Handheld museum.