In this talk I will present a short introduction to modified gravity models commonly discussed in the modern literature. Next, I shall focus on the recent results that I and my collaborators have obtained, concerning some novel observational probes of GR and some modified gravity models on cosmological scales. The new probes are based on observables that mostly have not been considered so far and will provide an additional constrains and an independent approach to classically used leansing and redshift space distortions methods.