Methods for moving drilled cuttings, the methods, in certain aspects, using a cuttings processor with a rotating annular screen to separate fluid from drilled cuttings and/or such methods including conveying with air under positive pressure, drilled cuttings to flow conduit apparatus; applying air under positive pressure to the flow conduit apparatus to continuously move the drilled cuttings material therethrough; continuously moving the drilled cuttings material with the air under pressure to separation apparatus; with the separation apparatus continuously separating drilled cuttings from air; wherein, in certain aspects, the drilled cuttings are included in a low density slurry with drilling fluid, drilling mud, and/or oil and wherein, in certain aspects, the separation apparatus is a cyclone separator and the drilled cuttings moved into the cyclone separator are wet; and systems for effecting such methods.