The authors study the controversial issues of termination of a criminal case (criminal prosecution) on the condition of voluntary compensation for the damage caused by the crime by the suspect (accused) during the preliminary investigation. The thesis is proved that in Russian criminal proceedings the procedure for voluntary compensation for damage caused by a crime is quite clearly regulated, and if the suspect (accused) voluntarily compensated for the property damage caused, then their actions will be evaluated within the current legal framework, when the fact of compensation for damage creates grounds for exemption from criminal liability and termination of the criminal case (criminal prosecution) in accordance with Articles 75, 76, 761, 762 of the Criminal Code of the Russian Federation, Articles 25, 251, 28, 281 of the Criminal Procedure Code of the Russian Federation.