Crypticity of biological invasions may blur invasion impacts and reduce their predictability. The impacts are often only detected in retrospect, and understood with delay, long after control measures would have been effective. Crypticity of biological invasions can be driven by inherent crypticity of alien species and their ecological functions and by time lags, spatio-temporal variability, and anthropogenic impacts. Considering crypticity in biological invasions would strongly enhance efficiency of monitoring and management planning. 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.