In this paper, for an arbitrary Kac-Moody Lie algebra
g
{\mathfrak g}
and a diagram automorphism
μ
\mu
of
g
{\mathfrak g}
satisfying certain natural linking conditions, we introduce and study a
μ
\mu
-twisted quantum affinization algebra
U
ℏ
(
g
^
μ
)
{\mathcal U}_\hbar \left (\hat {\mathfrak g}_\mu \right )
of
g
{\mathfrak g}
. When
g
{\mathfrak g}
is of finite type,
U
ℏ
(
g
^
μ
)
{\mathcal U}_\hbar \left (\hat {\mathfrak g}_\mu \right )
is Drinfeld’s current algebra realization of the twisted quantum affine algebra. When
μ
=
i
d
\mu =\mathrm {id}
and
g
{\mathfrak g}
in affine type,
U
ℏ
(
g
^
μ
)
{\mathcal U}_\hbar \left (\hat {\mathfrak g}_\mu \right )
is the quantum toroidal algebra introduced by Ginzburg, Kapranov and Vasserot. As the main results of this paper, we first prove a triangular decomposition for
U
ℏ
(
g
^
μ
)
{\mathcal U}_\hbar \left (\hat {\mathfrak g}_\mu \right )
. Second, we give a simple characterization of the affine quantum Serre relations on restricted
U
ℏ
(
g
^
μ
)
{\mathcal U}_\hbar \left (\hat {\mathfrak g}_\mu \right )
-modules in terms of “normal order products”. Third, we prove that the category of restricted
U
ℏ
(
g
^
μ
)
{\mathcal U}_\hbar \left (\hat {\mathfrak g}_\mu \right )
-modules is a monoidal category and hence obtain a topological Hopf algebra structure on the “restricted completion” of
U
ℏ
(
g
^
μ
)
{\mathcal U}_\hbar \left (\hat {\mathfrak g}_\mu \right )
. Last, we study the classical limit of
U
ℏ
(
g
^
μ
)
{\mathcal U}_\hbar \left (\hat {\mathfrak g}_\mu \right )
and abridge it to the quantization theory of extended affine Lie algebras. In particular, based on a classification result of Allison-Berman-Pianzola, we obtain the
ℏ
\hbar
-deformation of all nullity
2
2
extended affine Lie algebras.