The process of selection underpins many important questions facing those libraries which have responsibility for preservation. Properties of digital material present challenges to established preservation selection drivers and practices, including the increasing volume of digital material; the complexity of some digital objects; changing forms of cultural object creation and ownership; and the need for early interventions to keep material useable over time. This paper examines relevant library and related literature to identify and conceptualise factors which affect selection decision making relating to the preservation of digital material in libraries. It describes six organisational areas of concern: resources and volume; criteria; policy; legal and ethical issues; roles and responsibility; and user aspects of selection. Particular challenges include the need to revisit criteria and develop policies for preservation and selection along with the effect of unclear roles, responsibilities and expectations of a wide range of stakeholders.