The Chern-Schwartz-MacPherson (CSM) class of a compact (complex) variety X is a homology class which provides an analogue of the total Chern class of the tangent bundle of X, if X is singular. The CSM classes are determined by a functoriality property, and their existence was conjectured by Grothendieck and Deligne, and proved by MacPherson in 1970's. One can define a CSM class for any constructible subset of X, in particular for any Schubert cell in a generalized flag manifold G/P. I will explain how to calculate CSM classes of the Schubert cells, using the Bott-Samelson resolution of singularities. It turns out that the classes of Schubert cells are determined by certain Demazure-Lusztig operators in degenerate Hecke algebras; they are essentially equivalent to the characteristic cycles of the Verma modules in the cotangent bundle of the complete flag manifold, and to the (homological) stable envelopes of Maulik and Okounkov. Further, the expansion of CSM classes in Schubert classes is positive. The positivity property was proved earlier by J. Huh if X is a Grassmannian, and I will explain how one can prove this for arbitrary flag manifolds. This is based on two papers joint with Paolo Aluffi, and with Paolo Aluffi, Changjian Su and Jörg Schürmann.