Below, please find links to journals and presses that in my not-so-humble estimation, are publishing some of the most compelling stuff out there: 

Literary Journals

2River View   

Agni

Bellevue Literary Review                

Blackbird

Boulevard

Boxcar Poetry Review

Caketrain

Burnside Review

Cimarron Review

DIAGRAM

Drunken Boat

Ecotone

Guernica

jubilat

Linebreak

Mid-American Review

Mobius

Narrative Magazine

New York Quarterly

Nimrod International Literary Journal

Quarterly West

The Sycamore Review

Rattle

Tar River Poetry

The Apple Valley Review

Wising Up Press