Due to the current search of Majorana fermions, the physics of two-dimensional identical fermions with short-range p-wave interactions is of considerable interest. My talk will be about the effective theory of a chiral p+ip fermionic superfluid at zero temperature. This theory naturally incorporates the parity and time reversal violating effects such as the Hall viscosity and the edge current. I will present some applications of this theory such as the linear response to external electromagnetic and gravitational fields and the density profile of an isolated vortex. Finally, the dual gauge reformulation of this theory will be presented.