for grease from pans and such- i line a bowl with foil, and pour it in, directly from the pan. after it hardens, i ball up the foil and throw it away. i never put grease down the drain. i did once, in the first apartment i was in. it clogged the drain and the housing people were pissed.
for grease/oil/drippings from my little "george foreman grill"- i have an empty jar that i pour everything into. the grill has a little tray thing for drippings, i pour directly from the tray into the jar. because of the drippings/juice, it never hardens like plain grease does. so the jar keeps it contained, and it has a lid so there's no smell. once the jar gets full, i toss it in the trash.