On  manifolds  of  dimension  4,  Q  curvature  is  a  natural  extension  of  the  Gaussian curvature  on compact  surfaces.  In  this  talk,  we  will  survey  some  analytic  and  geometric  aspects  and  some recent study of Q curvature on manifolds of other dimensions. We will also discuss the study of the fractional Q curvature and connection to a class of non-local operators in conformal geometry.