Context. The Vela X-1 system is one of the best studied X-ray binaries, due to its early detection, persistent X-ray emission and a rich phenomenology at many wavelengths. The system is frequently quoted as an archetype of wind-accreting high-mass X-ray binaries and its parameters referred to as typical examples. Frequently though, specific values for these parameters have been used in subsequent studies, without full consideration of alternatives in the literature -even more so when results from one field of astronomy (e.g., stellar wind parameters) are used in another (e.g., X-ray astronomy). The issues and considerations discussed here for this specific, very well-known example will apply to various other X-ray binaries and the study of their physics. Aims. We aim to provide a robust compilation and synthesis of the accumulated knowledge about Vela X-1 as a solid baseline for future studies, adding new information, where available. Since this overview is targeted at a broader readership, we include more background information on the physics of the system and on methods than usually done. We also attempt to identify specific avenues of future research that could help to clarify open questions or determine certain parameters better than currently possible. Methods. We explore the vast literature for Vela X-1 and on modelling efforts based on this system or close analogues. We describe the evolution of the system knowledge over the decades and provide overview information on the essential parameters. We also add information derived from public data or catalogs to the data taken from the literature, especially data from the Gaia EDR3 release. Results. We derive an updated distance to Vela X-1 and update the spectra classification for HD 77518. At least around periastron, the supergiant star may be very close to filling its Roche lobe. Constraints on the clumpiness of the stellar wind from the supergiant star have improved, but tensions subsist. The orbit is in general very well determined, but a slight tension exists between the latest ephemerides. The orbital inclination remains the least certain factor and contributes significantly to the uncertainty in the neutron star mass. Estimates for the stellar wind terminal velocity and acceleration law have evolved strongly towards lower velocities over the years. Recent results with wind velocities at the orbital distance in the range or of or lower than the orbital velocity of the neutron star support the idea of transient wind-captured disks around the neutron star magnetosphere, for which observational and theoretical hints have emerged. Hydrodynamic models and observations are consistent with an accretion wake trailing the neutron star. Conclusions. With its extremely rich multi-wavelength observational data and wealth of related theoretical studies, Vela X-1 is an excellent laboratory to explore the physics of accreting X-ray binaries, especially in high-mass systems. Nevertheless, a lot of room remains to improve on the accumulated knowledge. On the observational...