Copulas are a useful tool to model multivariate distributions. While there exist various families of bivariate copulas, the construction of flexible and yet tractable copulas suitable for high-dimensional applications is much more challenging. This is even more true if one is concerned with the analysis of extreme values. In this paper, we construct a class of one-factor copulas and a family of extreme-value copulas well suited for high-dimensional applications and exhibiting a good balance between tractability and flexibility. The inference for these copulas is performed by using a least-squares estimator based on dependence coefficients. The modeling capabilities of the copulas are illustrated on simulated and real datasets.