This chapter studies regression models for a real variable with change of the parameters at unknown thresholds of the regressors or at an unknown sampling index. We first consider a linear regression and its empirical estimators with the least squares estimators of the change-point then the maximum likelihood estimators of parametric models. The convergence rates of the estimators are established. Least squares and likelihood ratio tests for the hypothesis of a constant mean are de fined accordingly, the weak convergence of the estimators and the test statistics under the hypothesis and alternatives are proved.