The number of biological invasions that occur each year is increasing and these new invasions are often associated with negative impacts. To alleviate the potential negative economic and environmental impacts of invasions surveillance strategies aim to improve the likelihood of identifying invasions early, thus increasing the probability of successful eradication efforts. Therefore, we designed and evaluated statistically-based surveillance strategies to optimize the detection of three case studies; two arthropod pests, grape phylloxera (Daktulosphaira vitifoliae Fitch) and Mediterranean fruit fly (Ceratitis capitata; Medfly) and one nematode pest, potato cyst nematode (Globodera rostochiensis; PCN). To best represent the basic biology and dispersal mechanisms of each pest we developed individual spread models and simulated the spread of each pest over the area of interest (e.g., field, town or region). Next we overlaid different surveillance strategies and recorded variables related to the time of detection and the total pest spread to determine the optimal surveillance strategy (i.e., the strategy with reduced spread and/or time to detection). Surveillance strategies included the surveillance strategy currently used for the pest and alternative strategies that varied survey location, frequency and density. For all case studies we determined that an alternative surveillance strategy could decrease the time to detection and/or the spread of the invasion for the same or a reduced effort. Specifically, surveillance strategies were optimized based on known habitat suitability (grape phylloxera), the location of high risk introduction sites and preferred hosts (Medfly) or increased surveillance density and/or surveys located predominantly in infested regions with limited random sampling in non-infested regions (PCN). Additionally, our findings may be applied to other biological invasions and we discuss how the results and/or models can be adapted to other regions, organisms and species.