Exterminating spiders?

most likely they want the moisture in the crawl space,use a bug bomb down there,they work pretty good,repeat once in awhile,should do the trick

I agree with the bug bomb answer, but you also need to knock down any webs and try to vacuum up egg sacks and nests (and then throw out the vacuum cleaner bag!). Spiders are something that needs to be constantly kept up on, or they'll keep coming back. One egg sac can release hundreds of younglings that will just keep reproducing and sometimes bombs and sprays don't kill the eggs. If you can't do this yourself (like if it's not your crawlspace), then you need to talk to your landlord and get him to do it.

Make sure you vacuum your apartment often and get into all the corners and under stuff like the sofa and bed. Also, if you're having a problem with them, be sure to shake out your clothing before you wear it and don't leave piles of clothing lying around. Spiders love to hide in clothes, particularily recluse spiders! And you don't want one of those nasty bites!!!