Parallels between physics and finance were established in a 100-year-long interaction of both disciplines. This study examines these parallels as well as research results on capital markets by statistical physics. The random walk, well known in physics, is also the basic model in finance. On this model is built the Black-Scholes theory of option pricing and hedging, or methods of risk control by diversification. The underlying assumptions are discussed using empirical financial data and analogies to physical models such as fluid flows, turbulence, or superdiffusion. On this basis, new theories of derivative pricing and of risk control can be formulated. Computer simulations of interacting agent models of financial markets provide insight into the origins of asset price fluctuations. Stock exchange crashes can be modelled in analogy to phase transitions and earthquakes. These models allow for predictions.