The topological string is a simplified version of physical string theory. It is of interest because it computes the BPS spectrum of relevant string theory compactifications, but also because it shares structural properties of physical string theory, Dualities and symmetries which often must be argued for arduously in the physical string can often be verified by computation in the topological setting. The central observable of the theory is the topological string partition function Z_top. This quantity has an eerie habit of making surprise appearances in many areas of mathematical physics. Numerous techniques exist for its computation in various expansions in parameters of the theory, yet to date, no satisfactory closed form for this quantity is known. In this talk, after reviewing notions of topological string theory with an emphasis on the interplay between worldsheet and target space physics (one of the structural similarities between the physical and the topological string alluded to above), I will report on progress in computing Z_top in settings where it is related to enigmatic 6d theories.