Relativistic MOND as an alternative to the dark matter paradigm

Milgrom's Modified Newtonian dynamics (MOND) provides an efficient way to summarize phenomenology of galaxies which does not lean on the notion of dark matter; it has great predictive power. Here I briefly review MOND as well as its implementation as a non relativistic modified gravity theory, AQUAL. Gravitational lensing and cosmology call for a relativistic gravity theory different front general relativity if dark matter is to be avoided. In recent years such a theory, TeVeS, has emerged from the marriage of AQUAL with the timelike vector field of Sanders. I discuss its structure and some of its successes and shortcomings.