The Compressed Baryonic Matter experiment (CBM) is a next-generation heavy-ion experiment to be operated at the FAIR facility, currently under construction in Darmstadt, Germany. A key feature of CBM is very high interaction rate, exceeding those of contemporary nuclear collision experiments by several orders of magnitude. Such interaction rates forbid a conventional, hardware-triggered readout; instead, experiment data will be freely streaming from self-triggered front-end electronics. In order to reduce the huge raw data volume to a recordable rate, data will be selected exclusively on CPU, which necessitates partial event reconstruction in real-time. Consequently, the traditional segregation of online and offline software vanishes; an integrated on- and offline data processing concept is called for. In this paper, we will report on concepts and developments for computing for CBM as well as on the status of preparations for its first physics run.