  In this paper we study singular kinetic equations on $\mathbb{R}^{2d}$ by the
paracontrolled distribution method introduced in \cite{GIP15}. We first develop
paracontrolled calculus in the kinetic setting, and use it to establish the
global well-posedness for the linear singular kinetic equations under the
assumptions that the products of singular terms are well-defined. We also
demonstrate how the required products can be defined in the case that singular
term is a Gaussian random field by probabilistic calculation. Interestingly,
although the terms in the zeroth Wiener chaos of regularization approximation
are not zero, they converge in suitable weighted Besov spaces and no
renormalization is required. As applications the global well-posedness for a
nonlinear kinetic equation with singular coefficients is obtained by the
entropy method. Moreover, we also solve the martingale problem for nonlinear
kinetic distribution dependent stochastic differential equations with singular
drifts.
