  We study 3d $\mathcal{N}=2$ supersymmetric gauge theories on closed oriented
Seifert manifold---circle bundles over an orbifold Riemann surface---, with a
gauge group G given by a product of simply-connected and/or unitary Lie groups.
Our main result is an exact formula for the supersymmetric partition function
on any Seifert manifold, generalizing previous results on lens spaces. We
explain how the result for an arbitrary Seifert geometry can be obtained by
combining simple building blocks, the "fibering operators." These operators are
half-BPS line defects, whose insertion along the $S^1$ fiber has the effect of
changing the topology of the Seifert fibration. We also point out that most
supersymmetric partition functions on Seifert manifolds admit a discrete
refinement, corresponding to the freedom in choosing a three-dimensional spin
structure. As a strong consistency check on our result, we show that the
Seifert partition functions match exactly across infrared dualities. The
duality relations are given by intricate (and seemingly new) mathematical
identities, which we tested numerically. Finally, we discuss in detail the
supersymmetric partition function on the lens space $L(p,q)_b$ with rational
squashing parameter $b^2 \in \mathbb{Q}$, comparing our formalism to previous
results, and explaining the relationship between the fibering operators and the
three-dimensional holomorphic blocks.
