Balancing treatment allocation over influential covariates is an important issue in clinical trials. In literature, a lot of covariate-adaptive designs are proposed for balancing covariates. In this talk, we consider the asymptotic properties of the covariate-adaptive designs. The asymptotic type I error and asymptotic power of hypothesis testing to compare the treatment effects under covariate-adaptive randomization procedures are considered. It is shown that the traditional test has not precise type I error and will lose power if the covariates are not balanced well. Basing on the asymptotic properties of a wide class of covariate-adaptive randomization procedures which can balance general covariate features, the asymptotically efficient covariate-adaptive designs are introduced so that the loss of power is asymptotically ignorable. The talk is based on works of Ma, Hu and Zhang (2015), Hu and Zhang (2013), Hu, Ye and Zhang (2022+), Ma, Li, Zhang and Hu (2022+).