Context. Both multi-messenger astronomy and new high-throughput wide-field surveys require flexible tools for the selection and analysis of astrophysical transients.Aims. Here we introduce the alert management, photometry, and evaluation of light curves (AMPEL) system, an analysis framework designed for high-throughput surveys and suited for streamed data. AMPEL combines the functionality of an alert broker with a generic framework capable of hosting user-contributed code; it encourages provenance and keeps track of the varying information states that a transient displays. The latter concept includes information gathered over time and data policies such as access or calibration levels.Methods. We describe a novel ongoing real-time multi-messenger analysis using AMPEL to combine IceCube neutrino data with the alert streams of the Zwicky Transient Facility (ZTF). We also reprocess the first four months of ZTF public alerts, and compare the yields of more than 200 different transient selection functions to quantify efficiencies for selecting Type Ia supernovae that were reported to the Transient Name Server (TNS).Results. We highlight three channels suitable for (1) the collection of a complete sample of extragalactic transients, (2) immediate follow-up of nearby transients, and (3) follow-up campaigns targeting young, extragalactic transients. We confirm ZTF completeness in that all TNS supernovae positioned on active CCD regions were detected.Conclusions. AMPEL can assist in filtering transients in real time, running alert reaction simulations, the reprocessing of full datasets as well as in the final scientific analysis of transient data. This is made possible by a novel way of capturing transient information through sequences of evolving states, and interfaces that allow new code to be natively applied to a full stream of alerts. This text also introduces a method by which users can design their own channels for inclusion in the AMPEL live instance that parses the ZTF stream and the real-time submission of high-quality extragalactic supernova candidates to the TNS.Key words: methods: data analysis / astronomical databases: miscellaneous / virtual observatory tools / supernovae: general / cosmology: observations⋆ Table A.1 is only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/631/A147