  Classical symmetric pairs consist of a symmetrizable Kac-Moody algebra
$\mathfrak{g}$, together with its subalgebra of fixed points under an
involutive automorphism of the second kind. Quantum group analogs of this
construction, known as quantum symmetric pairs, replace the fixed point Lie
subalgebras by one-sided coideal subalgebras of the quantized enveloping
algebra $U_q(\mathfrak{g})$. We provide a complete presentation by generators
and relations for these quantum symmetric pair coideal subalgebras. These
relations are of inhomogeneous $q$-Serre type and are valid without
restrictions on the generalized Cartan matrix. We draw special attention to the
split case, where the quantum symmetric pair coideal subalgebras are
generalized $q$-Onsager algebras.
