The notion of DLR measure in statistical mechanics of lattice spin systems was defined by the independent works developed by R.L. Dobrushin, and O.E. Lanford III with D. Ruelle, where were introduced the notion of Gibbsianness in terms of the study of probability measures that admits prescribed conditional probabilities with respect to the spin configurations outside of finite regions. We discuss in this talk generalizations of this notion in other areas of Mathematics, namely: Countable Markov Shifts and Groupoids. In the first part of the talk, we discuss results in collaboration with Eric O. Endo (USP) and Elmer Beltrán (USP) where a notion of infinite DLR measure is introduced and we proved that eigenmeasure of the Ruelle's operator is a DLR measure. The implication in the opposite direction is obtained for some cases. In the second part of the talk, if the time to allow us, we discuss the notion of DLR measure on groupoids of Deaconu-Renault and prove the equivalent result for this context, in other words, conformal measures are DLR measures. This last part is based on a work in progress with Rodrigo Frausino (USP), Thiago Raszeja (USP) and Ruy Exel (UFSC). These results will be part of a lecture of the last author at the ICM 2018.