Let G be the planar Galilean conformal algebra and $\widetilde{G}$ be its universal central extension. In this talk, we study universal and generic Whittaker G-modules (resp. $\widetilde{G}$-modules) of type $\phi$. We classify the isomorphism classes of universal and generic Whittaker modules. Moreover, we show that a generic Whittaker modules of type $\phi$ is irreducible if and only if $\phi$ is nonsingular. For the nonsingular case, we completely determine the Whittaker vectors in universal and generic Whittaker modules. For the singular case, we concretely construct some Whittaker vectors, which generate proper submodules of generic Whittaker modules. This is a joint work with Qiufan Chen and Hengyun Yang.

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