"Moroccan basket" covers a few genuinely different materials and shapes, and which one you want usually comes down to what it's actually going to hold, not just the look.
Palm leaf shopper baskets
Woven from palm leaf in the souks of Marrakesh, these are the style most people picture first — structured, with handles, originally a market bag rather than a home accessory. A handwoven shopper basket works the same way at home as it did at the market: shopping trips, beach days, or as a catch-all by the door for things you actually pick up and carry, since the handles and structure are built for that rather than for sitting still on a shelf.
Wicker storage trunks and baskets
For anything that's going to stay in one place — logs by a fireplace, throws, toys, laundry — a woven wicker trunk holds more and holds its shape better than a soft palm-leaf bag. The wicker storage trunk comes in three sizes, so it's worth measuring the actual space first: a small one under a console table reads as decor, while a large one doing real storage duty needs the room to match.
Trays and small baskets
Not every basket needs to be big. A wicker tray basket is the more useful size for a coffee table or bathroom shelf — remotes, cotton pads, whatever otherwise clutters a flat surface — and it's a lower-commitment way to bring the material into a room without a large basket dominating the space.
Beach and everyday bags
The same weaving shows up in bag form. Straw beach baskets are built lighter and more open than the storage pieces, since they're meant to be carried rather than sat in a corner — worth knowing if you were expecting the same sturdiness as a storage trunk in a bag.
Looking after them
Natural fibre baskets don't like damp. Keep them somewhere dry, and if one gets dusty, a soft brush or a dry cloth is enough — avoid soaking woven palm leaf or straw, since it can weaken the weave and cause it to lose its shape.