Over the last few years,algebraic topologists have grown increasingly interested in weighted projective spaces,and several new results have been obtained.I shall begin the talk with definitions,and compare some basic properties of the weighted and unweighted cases.In particular I shall consider the problem of imposing cellular structures,and describe how certain divisibility conditions on the weights allow a good solution.Less well-behaved weights present a greater challenge,although Kawasaki’s calculations of 1978 confirm that every case should admit a simple solution up to homotopy equivalence.Such solutions may in fact be read off from joint work with Tony Bahri,Matthias Franz,and Dietrich Notbohm - even though I failed to see this application for several years! I shall conclude by playing a game of weights with the audience; experience shows that this often leads to enlightenment.