The effect of heterogeneous environments upon the dynamics of invasion and the eradication or control of invasive species is poorly understood, although it is a major challenge for biodiversity conservation. Here, we first investigate how the probability and time for invasion are affected by spatial heterogeneity. Then, we study the effect of control program strategies (e.g. species specificity, spatial scale of action, detection and eradication efficiency) on the success and time of eradication. We find that heterogeneity increases both the invasion probability and the time to invasion. Heterogeneity also reduces the probability of eradication but does not change the time taken for successful eradication. We confirm that early detection of invasive species reduces the time until eradication, but we also demonstrate that this is true only if the local control action is sufficiently efficient. The criterion of removal efficiency is even more important for an eradication program than simply ensuring control effort when the invasive species is not abundant.