This Master's Thesis project is about various fundamental tools coming from statistical physics and complexity science in general, that are used to analyse economical and financial systems. In particular the dissertation focuses on the empirical study of financial data, employing different methods and ideas inspired by a physical approach to the analysis of complex systems: scaling relations, correlations and physics inspired modeling. Investigating the scaling properties of financial time series can give crucial insights about the underlying processes generating the empirical observations and can provide useful tools to detect consistent patterns across different scales. The analysis of the statistical relation between the price of different assets can offer the possibility to quantify their interactions and to extract the important information contained in the correlation structure of financial markets.