Tillage is an important weed control tool in organic farming. However, concerns about the negative impacts of tillage on soil quality and cropping system sustainability have prompted interest in weed management strategies that minimize soil disturbance. Past research indicated that the vegetative mulch produced by cover crops killed mechanically without tillage could provide moderately to fully acceptable levels of weed suppression. A multi-tactical approach is needed to achieve consistent weed control in organic, cover-crop based, conservation-agriculture systems. The objectives of current research include identifying optimal cover-crop kill methods, management timing of kill methods with crop species grown, and additional constraints that limit the use of killed cover crops for weed suppression in organic systems. This review paper summarizes progress over the past 20 years in developing conservation-agriculture, organic farming systems that use killed cover crops for weed suppression. Past and ongoing research will be summarized so that informed decisions can be made about adoption of this practice on certified organic farms.