Abstract Numerous spacecraft observations reveal that many heliospheric shocks are significantly affected by the presence of energetic particles such as solar energetic particles, pickup ions (PUIs), and anomalous cosmic rays. Examples include recent observations by the New Horizon spacecraft that show that the PUI pressure is larger than the thermal solar wind pressure in the solar wind. Voyager 2 observations of the heliospheric termination shock (HTS) show that it is completely mediated by suprathermal PUIs, and that the dissipation process at the HTS is not due to the thermal solar wind protons but to PUIs. We introduce a plasma model to study the structure of collisionless oblique magnetized shocks mediated by suprathermal energetic particles. We show that the incorporation of both collisionless heat flux and viscosity associated with energetic particles can completely determine the structure of collisionless oblique shocks for all angles except θ = 54.°7. The limitation at this angle is technical and comes in part from the assumed simplified form of the viscosity coefficient. In modeling the HTS, we show that PUIs are heated much more than the thermal gas through the HTS transition, and thus the HTS is mediated by PUIs. We study different values of the HTS obliquity and find that a parallel HTS heats PUIs more compared to the background thermal gas than it does at a perpendicular HTS.