The paper aims to offer an overview on some recent application of statistical physics methods to economic and financial problems, field known today as "econophysics". The second part introduces an example of microscopic modeling, namely the financial crashes seen as second order phase transitions. Although the model proposed is minimal -the Ising model in Bragg-Williams approximation- it leads to a discontinuity in the shape of the specific heat similar to the discontinuities of stock market índices during a financial crash.