We will introduce the topic on extreme values of the Riemann zeta function in the half critical strip. On the 1-line, we give a description of the error terms in the result by Aistleitner, Mahatab and Munsch. In the strip 1/2<Re s<1, we improve the result of Bondarenko and Seip in the caseσ↘1/2. The improvement is highly depended on the resonancemethod and a new estimate of the GCD sums.