Purple Sprouting Broccoli

Hi 

I'm quite new to gardening, grown a few bits last/this year which have done well (carrots, sweetcorn, tomatoes, lettuces, purple sprouting broccoli, herbs). Obviously the purple sprouting won't be ready until next spring but I'm just wondering if after I've harvested them all do I dig the plants up or leave them to grow again the next year??

Sorry to sound thick but I've looked for information about it and noone mentions what to do with the plants afterwards??

Thanks 
Liz

Excellent, thanks very much for your advice