This survey talk will be a review results obtained in collaboration with Mattias Franz and
Nigel Ray. As singular toric varieties, weighted projective spaces have an action of a real torus.
The equivariant cohomology with respect to this action is computed to be isomorphic to the
ring of piecewise polynomials on the defining fan. The theory is seen to parallel that for
smooth toric varieties with the  role of the Stanley-Reisner ring replaced by the ring of piecewise
polynomials. If time permits, an alternative presentation of weighted projective spaces as iterated
Thom complexes will be discussed briefly. Further collaboration with Mattias Franz, Nigel Ray and
Dietrich Notbohm yields in a complete topological classification of weighted projective spaces.