  We study the effective cones of cycles on universal hypersurfaces on a
projective variety $X$, particularly focusing on the case of universal
hypersurfaces in $\mathbb{P}^n$. We determine the effective cones of cycles on
the universal conic over $\mathbb{P}^2$. We also determine every effective cone
of cycles of dimension at most 6 or equal to 10 on any universal plane curve.
