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.Comment: 4 pages, 2 figures, Proceedings of the 7th European VLBI Network
Symposium held in Toledo, Spain on October 12-15, 2004. Editors: R.
Bachiller, F. Colomer, J.-F. Desmurs, P. de Vicent