Ecological effects of alien species can be dramatic, but management and prevention of negative impacts are often hindered by crypticity of the species or their ecological functions. Ecological functions can change dramatically over time, or manifest after long periods of an innocuous presence. Such cryptic processes may lead to an underestimation of long-term impacts and constrain management effectiveness. Here, we present a conceptual framework of crypticity in biological invasions. We identify the underlying mechanisms, provide evidence of their importance, and illustrate this phenomenon with case studies. This framework has potential to improve the recognition of the full risks and impacts of invasive species.