The prevalence of null results in searches for new physics at the LHC motivates the effort to make these searches as model-independent as possible. In this talk I will focus on three different approaches for being model-independent. First, I will describe procedures for adapting the Matrix Element Method for situations where the signal hypothesis is not known a priori. I will show general and intuitive approaches for performing analyses and presenting results, which involve the flattening of background distributions using likelihood information. Next I will present a sketch of how Voroni tessellations help to find some structural features like kinematic edges, boundaries in the collider data which might be present in new physics but not in Standard Model. I will show how these features can also be utilized to determine masses of new physics particles. Finally I will talk about the development in solving the combinatorial ambiguity which plays a crucial role to increase sensitivity of new physics signal and measure particle properties.