This thesis deals with analysis, forecasting and decision making in liberalised electricity markets. Particular focus is on wind power, its interaction with the market and the daily decision making of wind power generators. Among recently emerged renewable energy generation technologies, wind power has become the global leader in terms of installed capacity and advancement. This makes wind power an ideal candidate to analyse the impact of growing renewable energy generation capacity on the electricity markets. Furthermore, its present status of a significant supplier of electricity makes derivation of practically applicable tools for decision making highly relevant. The main characteristics of wind power differ fundamentally from those of conventional thermal power. Its effective generation capacity varies over time and is directly dependent on the weather. This dependency makes future production uncertain and difficult to contract even on a day-to-day basis. Consequently decisions about market bids for next-day delivery are based on production forecasts which are bound to come with some uncertainty. Naturally markets that experience large scale integration of wind power are affected by these different characteristics. The thesis presents analyses of how this impact is realised in markets significantly penetrated by wind power. Due to its representation by forecasts in the supply curve, such predictions are used to describe their non-linear influence on the market prices. Methods adequately accounting for this effect in models for day-ahead forecasting of the prices are also presented in the thesis. Prompted by the volatile behaviour of electricity markets, considerable focus has been on time-varying and robust parameter estimates. The models derived are all based on well know methods from the statistical literature. The stochastic production of wind turbines prompts the need for alternative methods for optimally bidding wind power to day-ahead markets. Such bidding strategies are formulated in this thesis, which utilise the information provided by the market models. Bids that maximise expected revenues are found and the possibility of risk averse behaviour is discussed.