Computability can be considered a natural next question after (constructive) existence in mathematics, dating back to Hilbert’s third question. In this talk, I will discuss computability questions associated to equilibrium states. More specifically, I will discuss some questions in Computability Theory arising in complex dynamics and ergodic theory. I will also give a brief introduction to general Computability Theory. Finally, we will show how to establish a uniformly machine to compute equilibrium state in uniformly expanding system and discuss some other applications and counterexamples.