We develop a new construction of complete non-compact 8-manifolds with Riemannian holonomy equal to Spin(7). As a consequence of the holonomy reduction, these manifolds are Ricci-flat. These metrics are built on the total spaces of principal T2-bundles over asymptotically conical Calabi Yau manifolds, and the result is generalized to orbifolds. The resulting metrics have a new geometry at infinity that we call asymptotically T2- fibred conical (AT2C) and which generalizes to higher dimensions the ALG metrics of 4-dimensional hyperkähler geometry, analogously to how ALC metrics generalize ALF metrics. As an application of this construction, we produce infinitely many diffeomor- phism types of AT2C Spin(7)-manifolds and the first known examples of complete toric Spin(7)-manifold. The talk is part of a series of lectures on the geometry of Riemannian manifolds with holonomy Spin(7) during the week Nov 24-28. The event is part of the activities of the FIS2 project BeyondCY3. More information available at: https://sites.google.com/uniroma1.it/lfoscolo/fis2-beyondcy3/events