We focus on the linear model with conditional heteroskedasticity of unknown form. "Adaptive" estimators of the coefficients of the linear model, based on no rigid parameterisation of the heteroskedasticity, but having the same asymptotic efficiency as estimators which do use such information, are surveyed. A small Monte Carlo study of their performance is reported. We describe a modification of the popular paradigm in which the variance is a function of the mean, allowing this function to be of unknown form. We describe a modification also of the autoregressive conditional heteroskedasticity (ARCH) model, in which the heteroskedasticity function is of unknown form.We focus on the linear model with conditional heteroskedasticity of unknown form. "Adaptive" estimators of the coefficients of the linear model, based on no rigid parameterisation of the heteroskedasticity, but having the same asymptotic efficiency as estimators which do use such information, are surveyed. A small Monte Carlo study of their performance is reported. We describe a modification of the popular paradigm in which the variance is a function of the mean, allowing this function to be of unknown form. We describe a modification also of the autoregressive conditional heteroskedasticity (ARCH) model, in which the heteroskedasticity function is of unknown form.