2D continuum Gaussian free field (GFF) is a canonical model for random surfaces. It has various nice properties like conformal invariance or the Markov property, but also a notable disadvantage when thought of as a surface - it is merely a random generalized function that cannot be defined pointwise. Nevertheless, when one is stubborn enough and insists on studying its geometry, beautiful things start to appear: for example, connections to SLE processes of Schramm or to Brownian loop soups. I would like to give a short overview of some of the results obtained in this direction in collaboration with T. Lupu, E. Powell, A. Sepulveda and W. Werner. In particular, I would like to explain how to decompose the 2D continuum GFF into an independent sum of measures.