Torching the fruits of your labor
Some vegetables can be grilled as is and some need a bit of preliminary blanching in the kitchen. If you have the time, you can also put a pot of water on the grill and pre-cook the veggies there. Some of the vegetables which require blanching include artichokes, carrots, fennel, leeks (large ones), potatoes.
Novice grillers will probably want to start with onions, leeks or peppers. The more experienced chef can move into eggplant, carrots, scallions, zucchini, corn-on-the-cob, potatoes, artichokes, celery, cucumbers, fennel, jicama, mushrooms, garlic, rhubarb and tomatoes (skewer if very small). All of the above item can be brushed or dipped in olive oil (or some other oil) so they dont get charred, burned nor lose much moisture content.
For the rounder veggies such as eggplant, zucchini, cucumbers, potatoes, etc. you want to cut them in half or quarters so that theres still some bulk to stop them from falling through the grilling surface. Also with this kind of cutting you avoid the immediate disintegration of a wafer thin slice.