Most carry those soft style flight bags (you know, like a laptop bag, but bigger). You must carry your licence and a torch but in addition the typical flight bag carries sunglasses, magazines, a laptop, personal bottle of water, calculator and not much else. For longhaul you can carry a t-shirt and shorts to sleep in during crew rest.
There is plenty of room in the cockpit for each pilot to carry flight bag, be it a big traditional hard leather one or smaller...and room for some shopping bags on the way home too!