  We consider three-dimensional ${\mathcal N}=2$ supersymmetric field theories
defined on general complex-valued backgrounds of Euclidean new minimal
supergravity admitting two Killing spinors of opposite $R$-charges. We compute
partition functions for theories defined on general circle bundles over
spindles $\Sigma$, including $\Sigma\times S^1$ as well as branched and
squashed lens spaces, thus obtaining novel observables characterizing
three-dimensional supersymmetric gauge theories. We discuss both twisted and
anti-twisted theories compactified on $\Sigma\times S^1$ and demonstrate that
their partition functions are encoded by a single formula that we refer to as
the spindle index, unifying and generalizing superconformal and topologically
twisted indices in the limit where orbifold singularities are absent.
Furthermore, we test our new index using non-perturbative dualities and obtain
one-loop determinants of two-dimensional supersymmetric gauge theories
compactified on the spindle.
