  We perform SUSY localization for Coulomb branch operators of 3d
$\mathcal{N}=4$ gauge theories in $\mathbb{R}^3$ with $\Omega$-deformation. For
the dressed monopole operators whose expectation values do not involve
non-perturbative corrections, our computations reproduce the results of the
so-called abelianization procedure. For the expectation values of other
operators and the correlation functions of multiple operators in $U(N)$ gauge
theories, we compute the non-perturbative corrections due to monopole bubbling
using matrix models obtained by brane construction. We relate the results of
localization to algebraic structures discussed in the mathematical literature,
and also point out a similar relation for line operators in 4d $\mathcal{N}=2$
gauge theories. For $U(N)$ (quiver) gauge theories in 3d we demonstrate a
direct correspondence between wall-crossing and the ordering of operators.
