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Over the last 25 years Monte Carlo programs were being developped in Cracowin the group guided by Prof. Stanislaw Jadach. Many of those programs becamestandard in their application domains. In the following let us review someaspects of such projects which were probably at the foundation of theirsuccess. We will concentrate on mathematical aspects of their design andhistory of their construction. It is rather difficult to cover 25 years of theresearch in a single talk. That is why, I have organized my presentation aroundMonte Carlo PHOTOS but stressing its relation to other activities and projectsoften realized together with Prof. Jadach. Many of omitted aspects will findtheir way into other perentations collected in this volume.  I will concentrate on issues related to phasespace parametrization and spinamplitudes as used in our Monte Carlo programs such as MUSTRAAL, TAUOLA or KKMCand their similarities and differences with respect to solution used in PHOTOS.

Historical and mathematical aspects of iterative solutions for Monte Carlo simulations