Self-driving vehicles have become a reality. For instance, in the summer of 2017, self-driving buses carried passengers on a designated route in Estonia's capital Tallinn. Regrettably, traffic accidents involving self-driving vehicles have also become a reality. This article focuses on fully autonomous vehicles. The safe and responsible use of fully autonomous vehicles calls for appropriate rules and an appropriate allocation of liability. Above all, fully autonomous vehicles pose a challenge to the law of delict. The article seeks to establish, based on the example of Estonian law, whether the application of delictual liability is affected by the autonomy of a vehicle and, if so, whether related differences are significant, and whether the law of delict needs to be modified in the light thereof. The issues are discussed primarily in the context of Estonian law, but parallels with German law are drawn as well. The conclusions drawn are more or less universal and can be taken into account also in other jurisdictions besides Estonia. The article analyses liability for damage caused by fully autonomous vehicles under general delictual liability, strict liability and product liability.