Our project MOMO (Multiwavelength observations and modelling of OJ 287) consists of dedicated, dense, long-term flux and spectroscopic monitoring and deep follow-up observations of the blazar OJ 287 at >13 frequencies from the radio to the X-ray band since late 2015. In particular, we are using Swift to obtain optical-UV-X-ray spectral energy distributions (SEDs) and the Effelsberg telescope to obtain radio measurements between 2 and 40 GHz. MOMO is the densest long-term monitoring of OJ 287 involving X-rays and broad-band SEDs. The theoretical part of the project aims at understanding jet and accretion physics of the blazar central engine in general and the supermassive binary black hole scenario in particular. Results are presented in a sequence of publications and so far included: detection and detailed analysis of the bright 2016/17 and 2020 outbursts and the long-term light curve; Swift, XMM and NuSTAR spectroscopy of the 2020 outburst around maximum; and interpretation of selected events in the context of the binary black hole scenario of OJ 287 (papers I-IV). Here, we provide a description of the project MOMO, a summary of previous results, the latest results, and we discuss future prospects.