Classically, Kazhdan-Lusztig theory for a Kac-Moody group establishes deep connections between the geometry of the associated (complex) flag ind-variety, the representations of the associated Kac-Moody Lie algebra, and the structure of a Hecke algebra, which is constructed solely from its Weyl group and has a very combinatorial nature. Whereas an affine version of the two former objects have yet to be defined for non-reductive Kac-Moody groups, Braverman, Kazhdan Patnaik and Bardy-Panse Gaussent Rousseau have independently constructed the affine analog of the Hecke algebra for Kac-Moody groups. It is called the Iwahori-Hecke algebra and has a basis indexed by the affinized Weyl semigroup we introduced last week. For reductive groups, it is a well known object fundamental to the study of p-adic reductive groups. For non reductive Kac-Moody groups, Muthiah initiated in 2019 the development of an affine Kazhdan-Lusztig theory using this new Iwahori-Hecke algebra and masures, it was also the main focus of my PhD. The hyperspecial analog to affine Kazhdan-Lusztig theory is the Satake equivalence, which was recently given a geometric meaning by Bouthier and Vasserot in the Kac-Moody setting. In this talk, I will present some aspects of these three theories.