There is abundant evidence that the mass of the Universe is dominated by dark matter of unknown form. The MACHO project is one of several teams searching for the dark matter around our Galaxy in the form of Massive Compact Halo Objects (MACHOs). If a compact object passes very close to the line of sight to a background star, the gravitational deflection of light causes an apparent brightening of the star, i.e. a gravitational `microlensing' event. Such events will be very rare, so millions of stars must be monitored for many years. We describe our search for microlensing using a very large CCD camera on the dedicated 1.27m telescope at Mt. Stromlo, Australia: currently some 14 events have been discovered towards the Large Magellanic Cloud. The lack of short-timescale events excludes planetary mass MACHOs as a major contributor to the dark matter, but the observed long events (durations 1--6 months) suggest that a major fraction may be in fairly massive objects $\sim 0.5 \Msun$. It is currently difficult but not impossible to explain these events by other lens populations; we discuss some prospects for clarifying the nature of the lenses.

RevTex, 20 pages incl. 11 Postscript figures. Rev. Mod. Phys. 'Colloquium' article, to appear Jan. 1999