ESO's La Silla Paranal Observatory operates some of the most advanced and scientifically productive facilities currently available to astronomers: the optical/infrared VLT, VLTI and survey telescopes on Paranal, the optical/infrared NTT and the 3.6m telescopes on La Silla and the APEX single dish on Chajnantor. Its science operations are embedded in an end-to-end data flow system that encompasses the entire lifecycle of scientific data, from the preparation of observing proposals to telescope scheduling, from the detailed definition of observing strategies to their execution at the telescope, from data processing to archival exploitation of the data. In this contribution we present the current status, prospects and strategies of the back-end segment of the La Silla Paranal Observatory science operations, namely data transfer form the observatory, data processing for quality control and science purposes, and the ESO Science Archive Facility.