There are many traffic situations where a driver has to decide whether a manoeuvre is safe to perform based on the information available to them in peripheral vision. Such information is surprisingly limited and people are routinely unaware of these limitations. In a series of experiments we asked drivers in a high-resolution driving simulator to decide whether oncoming vehicles were present. Vehicles could appear anywhere in an arc of 194 degrees of visual angle and were always clearly detectable using central vision. Even when drivers were free to make as many head movements as they wanted, we found that they made regular errors (failures to detect an oncoming vehicle). Most of these errors occurred when target vehicles initially appeared in the extreme periphery (beyond 60 degrees to the right or left). These errors were frequent when the oncoming vehicle was a motorcycle, and less common when the oncoming vehicle was a truck. Recordings of drivers' head and eye movements suggested that they typically perform this task by making only two or three head movements (similar to what a driver might do at a real junction) and they do not always need to fixate directly on a vehicle to know that it is there. The problem is that even after a head and eye movement to one side, extreme locations may still be viewed using peripheral vision. Such vision may be good enough to detect a large truck, but not a smaller motorcyclist. This is consistent with our finding that when drivers explicitly search for a motorcyclist these peripheral errors are dramatically reduced. This may be a major cause of real-world crashes where oncoming motorcyclists are involved and where the driver is an older one with potentially reduced neck mobility. We provide suggestions for interventions that might prevent these crashes.