One of the common forms of street crime in The Amazing Spider-Man are car chases (high speed pursuits). Luckily, these are pretty easy to take care of!
Street Crime Guide: Car Chase
First, look for a blue car icon on the map, then use the R1 button to target the cop car found there and start the event. Immediately the crooks will begin to speed away, so try to get atop their car with web rush. If they make it around a corner, start swinging towards them, then descend from above.
Once atop the car, hammer away on the web shoot button to clutter up the windowshield. One crook will try to take Spidey down with a shotgun blast to the head, so make sure to dodge! Then finish webshooting the car, and put these crooks away for good!