Designing group key management schemes is a troubled field. In this paper, we review three schemes recently proposed, including Kayam's scheme for groups with hierarchy, Piao's group key management (KM) scheme, Purushothama's group KM schemes. We point out the problems in each scheme. Kayam's scheme is not secure to collusion attack. Piao's group KM scheme is not secure. The hard problem it bases is not really hard, and the way their scheme uses a hard problem is improper. Purushothama's scheme has an unnecessary design that costs lots of resources and does not give an advantage to the security level and dynamic efficiency of it. We also briefly analyze the underlying reasons why these problems emerge and give suggestions on designing. Copyright © 2014 John Wiley & Sons, Ltd.