We elaborate on the construction of de Sitter solutions from IIA orientifolds
of SU(3)-structure manifolds that solve the 10-dimensional equations of motion
at tree-level in the approximation of smeared sources. First we classify
geometries that are orbifolds of a group manifold covering space which, upon
the proper inclusion of O6 planes, can be described within the framework of N=1
supergravity in 4D. Then we scan systematically for de Sitter solutions,
obtained as critical points of an effective 4D potential. Apart from finding
many new solutions we emphasize the challenges in constructing explicit
classical de Sitter vacua, which have sofar not been met. These challenges are
interesting avenues for further research and include finding solutions that are
perturbatively stable, satisfy charge and flux quantization, and have genuine
localized (versus smeared) orientifold sources. This paper intends to be
self-contained and pedagogical, and thus can serve as a guide to the necessary
technical tools required for this line of research. In an appendix we explain
how to study flux and charge quantization in the presence of a non-trivial
H-field using twisted homology.Comment: 50 pages, 3 figure