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In this paper, we study the thermodynamic features of a rotating black holesurrounded by perfect fluid dark matter. We analyze the critical behavior ofthe black hole by considering the known relationship between pressure andcosmological constant. We show that the black hole admits a first order phasetransition and, both rotation and perfect fluid dark matter parameters have asignificant impact on the critical quantities. We also introduce a new ad hocpressure related to the perfect fluid dark matter and find a first order vander Waals like phase transition. In addition, using the sixth order WKB method,we investigate the massless scalar quasinormal modes (QNMs) for the staticspherically symmetric black hole surrounded by dark matter. Using the finitedifference scheme, the dynamical evolution of the QNMs is also discussed fordifferent values of angular momentum and overtone parameters.

Instability and phase transitions of a rotating black hole in the presence of perfect fluid dark matter