My experience is that the longer it sits around before cooking, the more bitter it will get, so cook it as soon as possible after purchase.
The bitterness can be knocked down quite a bit by salting slices for a while, as mentioned above.
When making eggplant Parmesan; after salting, rinsing, and drying, a standard dip in beaten egg and a dredge through breadcrumbs before sauteing makes a nice crunchy disc.
Just a couple weekends ago, the wife brought a couple home with some zucchini. Ratatouille time.
Ratatouille:
1 large or 2 small eggplant, diced 3/4 - 1 inch
2 med or 1 large onion, large diced
2 zucchini, sliced into rounds
2 - 3 bell pepper (red, yellow green makes a nice mix) diced
4 -6 cloves garlic fine diced (at least: garlic don't need a reason)
1 28 oz can crushed tomatoes
2 cups chicken or vegetable stock
Olive oil for sauteing
Salt & pepper to taste
In a large heavy pot, at least 6 quarts, heat olive oil and sweat onions, adding salt & pepper as needed. When onions are about half done, add bell peppers and saute until both are softened but not caramelized, again adding S&P as needed. When just done, clear a space in the bottom of the pot, add a bit of oil and add the crushed garlic. When the garlic just starts getting fragrant, add the crushed tomatoes to prevent the garlic from burning, and stir in. Add the diced eggplant and zucchini, stir together, and add enough stock to cover everything. Simmer until eggplant is softened, stirring occasionally, approximately 1 hour. Can be simmered covered and uncovered to regulate amount of liquid, as the eggplant and zucchini will release some as they cook. Will be even better the next day as the flavors will combine and mellow.