Abstract:  Equations in words and equations in free groups are very close in nature. They are objects of a natural interest for logicians, discrete mathematicians and computer scientists. On the other hand, they are related to several other topics in mathematics; for example, to groups acting on R-trees and decision problems for knots in 3-manifolds. I will discuss these relations and computational complexity of equations solvability. In particular, a recent result on NP-completeness of solvability of equations in free groups will be discussed.