  A loop is a rather general algebraic structure that has an identity element
and division, but is not necessarily associative. Smooth loops are a direct
generalization of Lie groups. A key example of a non-Lie smooth loop is the
loop of unit octonions. In this paper, we study properties of smooth loops and
their associated tangent algebras, including a loop analog of the Mauer-Cartan
equation. Then, given a manifold, we introduce a loop bundle as an associated
bundle to a particular principal bundle. Given a connection on the principal
bundle, we define the torsion of a loop bundle structure and show how it
relates to the curvature, and also consider the critical points of some related
functionals. Throughout, we see how some of the known properties of
$G_{2}$-structures can be seen from this more general setting.
