Poetry Magazine was founded in Chicago by Harriet Monroe in 1912. The magazine established a reputation early on by publishing many important poems of T.S. Eliot, Ezra Pound, Marianne Moore, Wallace Stevens, William Carlos Williams, and many others.
Since then it has presented, sometimes for the first time, poems by almost every significant poet of the 20th century. They also have published poetry by famous non poets. They have good distribution and you can find Poetry Magazine at most newstands and bookstores that carry literary journals.
They have made a great deal of the work they have published available for free online, so it is relatively easy to get a feeling for what they publish currently. They do not accept previously published work. That includes work published on your personal blog or Facebook.
Poetry Magazine pays a minimum of $300 for poetry. They accept all submissions via the easy to use submission manager Submittable. They recently started to accept visual poetry.
They try to respond to all submissions within six months, although it is often longer than that. They receive a large number of submissions and reject the vast majority of what is submitted to them.
To learn more visit their submission guidelines here.