  Let $(\bf U, \bf U^\imath)$ be a quantum symmetric pair of Kac-Moody type.
The $\imath$quantum groups $\bf U^\imath$ and the universal $\imath$quantum
groups $\widetilde{\bf U}^\imath$ can be viewed as a generalization of quantum
groups and Drinfeld doubles $\widetilde{\bf U}$. In this paper we formulate and
establish Serre-Lusztig relations for $\imath$quantum groups in terms of
$\imath$divided powers, which are an $\imath$-analog of Lusztig's higher order
Serre relations for quantum groups. This has applications to braid group
symmetries on $\imath$quantum groups.
