Not much is known about lay public perceptions of non-native species and their underlying values. Public awareness and engagement, however, are important aspects in invasive species management. In this study, we examined the relations between the lay public's visions of nature, their knowledge about non-native species, and their perceptions of non-native species and invasive species management with a survey administered in the Netherlands. Within this framework, we identified three measures for perception of non-native species: perceived risk, control and engagement. In general, respondents scored moderate values for perceived risk and personal engagement. However, in case of potential ecological or human health risks, control measures were supported. Respondents' images of the human-nature relationship proved to be relevant in engagement in problems caused by invasive species and in recognizing the need for control, while images of nature appeared to be most important in perceiving risks to the environment. We also found that eradication of non-native species was predominantly opposed for species with a high cuddliness factor such as mammals and bird species. We conclude that lay public perceptions of non-native species have to be put in a wider context of visions of nature, and we discuss the implications for public support for invasive species management.