Whether or not there is a break in transmission of the lexifier language has joined the question of substrate influence in being among the most contentious issues in pidgin and creole studies. This chapter first examines the two main views regarding the transmission of the lexifier language in relation to creole genesis. It then looks at debates about the transmission of substrate features into creoles via language transfer. These analyses are followed by a discussion of the implications of the different views with regard to colonial and postcolonial ideologies, and current views of agency and identity in studies of second language acquisition.