Abstract: The Russian scientist of mathematics and medanics G.V. Kolosovintroduced firstly the complex variable method to solve two-dimensionalelasticity problems in 1909, which was thenextended to fracture mechanics problems. In the past 100years, the complex variable method has made great progresses.This year is the hundredth anniversary ofthe complex variable method of elasticity and fracture mechanics. Thismemorial paper summarizes research progresses of complex variablemethod in classical fracture mechanics, composite materials fracturemechanics, noval materials fracture mechanics and fracture problems for threedimensinal bodies.