In the case of damage caused by a conventionally driven vehicle, it is usually possible in EU Member States to subject the possessor/controller of the vehicle to heightened tortious no-fault liability, i.e. strict liability. The development and possible introduction of self-driving vehicles pose a challenge also for tort law, because it is unlikely that self-driving vehicles will not cause any damage to third parties. With the application of strict liability in mind, this article attempts to identify possible differences between damage caused by a conventional vehicle as opposed to that caused by a self-driving vehicle. In light of this developing technology the key legislative question to be answered is whether the introduction of self-driving vehicles calls for, among other things, the revision of strict liability rules. Answers to these questions are sought mainly based on Estonian tort law.