Towards the event horizon - the vicinity of AGN at micro-arcsecond resolution

We summarize the present status of VLBI experiments at 3 mm (86 GHz), 2 mm (129-150 GHz) and 1.3 mm (215-230 GHz). We present and discuss a new 3 mm VLBI map of M87 (Virgo A), which has a spatial resolution of only approx. 20 Schwarzschild radii. We discuss recent VLBI results for SgrA* and argue in favor of new observations within an extended European mm-VLBI network, in order to search for variability. We discuss the possibilities to image the `event horizon' of a super-massive black hole at wavelengths < 2mm, and conclude that the addition of large and sensitive millimetre telescopes such as CARMA, the SMA, the LMT and ALMA will be crucial for this.