Hosta and lillies are the flowers that i’m wondering about.

I have lillies, they are all done blooming and are now just an ugly stem. What do I do now? Do I cut them down or let them go? They were already here when I moved in to this house. I’ve never had them before.
http://images.search.yahoo.com/search/images/view?back=http%3A%2F%2Fimages.search.yahoo.com%2Fsearch%2Fimages%3Fp%3Dyellow%2Blilies%26ei%3DUTF-8%26js%3D1%26ni%3D18%26fr%3Dyfp-t-501%26b%3D73&w=500&h=375&imgurl=static.flickr.com%2F48%2F189101725_ba8091683f_m.jpg&rurl=http%3A%2F%2Fwww.flickr.com%2Fphotos%2F58797022%40N00%2F189101725%2F&size=193.2kB&name=189101725_ba8091683f.jpg&p=yellow+lilies&type=jpeg&no=86&tt=12,042&oid=7bb45307900f0f08&fusr=1SASSYGAL&tit=yellow+lilies&hurl=http%3A%2F%2Fwww.flickr.com%2Fphotos%2F58797022%40N00%2F&ei=UTF-8&src=p these are what the lilies I have look like.