Schur Q-functions are a family of symmetric functions introduced by Schur in his study of projective representations of symmetric groups. They are obtained by putting t = -1 in the Hall-Littlewood functions associated to the root system of type A. (Schur functions are the t = 0 specialization.) This talk concerns symplectic Q-functions, which are obtained by putting t = -1 in the Hall-Littlewood functions associated to the root system of type C. We present several Pfaffian formulas for symplectic Q-functions similar to those for Schur Q-functions and give a tableau description. Also we discuss some conjectures including the positivity conjecture of structure constants.