Apparatuses and methods for heating moving continuous glass ribbons at desired lines of separation and/or for separating glass sheets from continuous glass ribbons are disclosed. An apparatus includes a translatable support portion and a heating apparatus coupled to the support portion. The heating apparatus is configured to contact the continuous glass ribbon across at least a portion of a width of the continuous glass ribbon at the desired line of separation as the support portion moves in a draw direction, thereby preferentially applying heat to a first side of the continuous glass ribbon at the desired line of separation as the continuous glass ribbon moves in the draw direction.