In 1900, David Hilbert delivered an address to the International Congress of Mathematics in Paris, citing 23 problems which acted as a spur for much work in the 20th century. The questions varied from specific mathematical questions to programmes of research. The main areas of work were in algebraic number theory, logic, and topology, which was at an early stage of development. Each problem is stated and a short commentary on progress is given. Most, though not all, such as the Riemann hypothesis have been solved; a few problems were poorly formulated.