Astronomers have long known that galaxies and clusters would fly apart unless they were held together by the gravitational pull of much more material than we actually see.
The strength of the case built up gradually. The argument that clusters of galaxies would be unbound without dark matter dates back to Zwicky (1937) and others in the 1930s. Kahn and Woltjer (1959) pointed out that the motion of Andromeda towards us implied that there must be dark matter in our Local Group of galaxies. But the dynamical evidence for massive halos (or `coronae') around individual galaxies firmed up rather later (e.g. Roberts and Rots 1973, Rubin, Thonnard and Ford 1978).
Two 1974 papers were specially influential in the latter context. Here is a quote from each:
The mass of galactic coronas exceeds the mass of populations of known stars by one order of magnitude, as do the effective dimensions. .... The mass/luminosity ratio rises to f = 100 for spiral and f = 120 for elliptical galaxies. With H = 50 km/sec/Mpc this ratio for the Coma cluster is 170 (Einasto, Kaasik and Saar 1974).
Currently-available observations strongly indicate that the mass of spiral galaxies increases almost linearly with radius to nearly 1 Mpc.... and that the ratio of this mass to the light within the Holmberg radios, f, is 200 (M / L). (Ostriker, Peebles and Yahil, 1974).
The amount of dark matter, and how it is distributed, is now far better established than it was when those papers were written. The immense advances in delineated dark matter in clusters and in individual galaxies are manifest in the programme for this meeting. The rapid current progress stems from the confluence of several new kinds of data within the same few-year interval: optical surveys of large areas and high redshifts, CMB fluctuation measurements, sharp X-ray images, and so forth.
The progress has not been solely observational. Over the last 20 years, a compelling theoretical perspective for the emergence of cosmic structure has been developed. The expanding universe is unstable to the growth of structure, in the sense that regions that start off very slightly overdense have their expansion slowed by their excess gravity, and evolve into conspicuous density contrasts. According to this `cold dark matter' (CDM) model, the present-day structure of galaxies and clusters is moulded by the gravitational aggregation of non-baryonic matter, which is an essential ingredient of the early universe (Pagels and Primack 1982, Peebles 1982, Blumenthal et al. 1984, Davis et al. 1985). These models have been firmed up by vastly improved simulations, rendered possible by burgeoning computer power. And astronomers can now compare these `virtual universes' with the real one, not just at the present era but (by observing very distant objects) can probe back towards the formative stages when the first galaxies emerged.
The following comments are intended to provide a context for the later papers. (For that reason, I do not give detailed references to the topics covered by other speakers - just some citations of historical interest).