Class. Quantum Grav. 16 (1999) A37–A75. Printed in the UK PII: S0264-9381(99)00323-8 83 years of general relativity and cosmology: progress and problems George F R Ellis Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, Cape Town, South Africa E-mail: ellis@maths.uct.ac.za Received 22 December 1998 Abstract. This paper considers the evolution of the relation between gravitational theory and cosmology from the development of the first simple quantitative cosmological models in 1917 to the sophistication of our cosmological models at the turn of the millenium. It is structured around a series of major ideas that have been fundamental in developing today’s models, namely: 1, the idea of a cosmological model; 2, the idea of an evolving universe; 3, the idea of astronomical observational tests; 4, the idea of physical structure development; 5, the idea of causal and visual horizons; 6, the idea of an explanation of spacetime geometry; and 7, the idea of a beginning to the universe. A final section considers relating our simplified models to the real universe, and a series of related unresolved issues that need investigation. PACS numbers: 0420, 9880 Contents Contents 37 1. Introduction 39 2. The idea of a cosmological model 39 2.1. The nature of cosmological modelling 40 2.2. Unchanging spacetimes 40 3. The idea of the evolving universe 41 3.1. Robertson–Walker geometry and time evolution 41 3.2. Friedmann–Lemaˆıtre dynamics 42 3.3. The hot big bang and ages 43 4. The idea of astronomical observational tests 45 4.1. FL observations 45 4.2. Observations of distant sources 46 4.3. Background radiation 48 4.4. RW topology 48 4.5. The observational predicament 49 5. The idea of physical structure development 49 5.1. Before decoupling: particles and radiation 50 5.2. After decoupling: astronomical structure formation 51 5.3. The arrow of time 53 5.4. Physical cosmology 53 0264-9381/99/SA0037+39$30.00 © 1999 IOP Publishing Ltd A37