The unknotting number of a knot is the minimum number of times that the knot must be passed through itself in order to untie it. The unknotting conjecture states that the unknotting number of a knot obtained by tying two knots in sequence along a string is equal to the sum of the unknotting numbers of the two knots. In this ongoing joint work with Wenzhao Chen, we study symmetric unknotting numbers for knots with a particular type of symmetry. We relate these symmetric unknotting numbers to some classical questions in knot theory, and we prove that the symmetric version of the unknotting conjecture is false.