  We combine theory and experiments to explore the kinematics and actuation of
intrinsically curved folds (ICFs) in otherwise developable shells. Unlike
origami folds, ICFs are not bending isometries of flat sheets, but arise via
non-isometric processes (growth/moulding) or by joining sheets along curved
boundaries. Experimentally, we implement both, first making joined ICFs from
paper, then fabricating flat liquid crystal elastomer (LCE) sheets that morph
into ICFs upon heating/swelling via programmed metric changes. Theoretically,
an ICF's intrinsic geometry is defined by the geodesic curvatures on either
side, $\kappa_{g_i}$. Given these, and a target 3D fold-line, one can construct
the entire surface isometrically, and compute the bending energy. This
construction shows ICFs are bending mechanisms, with a continuous family of
isometries trading fold angle against fold-line curvature. In ICFs with
symmetric $\kappa_{g_i}$, straightening the fold-line culminates in a
fully-folded flat state that is deployable but weak, while asymmetric ICFs
ultimately lock with a mechanically strong finite-angle. When unloaded,
freely-hinged ICFs simply adopt the (thickness $t$ independent) isometry that
minimizes the bend energy. In contrast, in LCE ICFs a competition between flank
and ridge selects a ridge curvature that, unusually, scales as $t^{-1/7}$.
Finally, we demonstrate how multiple ICFs can be combined in one LCE sheet, to
create a versatile stretch-strong gripper that lifts $\sim$40x its own weight.
