The aim of this book is to estimate the conditional mean of some functions depending on the response variable Y (moments, distributions...) in regression models where this response is possibly censored. In parametric regression, polynomial and nonlinear conditional means are estimated in a new way while, in nonparametric regression, some new estimators are provided to approximate general L-functionals (conditional mean, trimmed mean, quantiles...). The ideas developed in those methods lead to establish more general results in nonparametric estimation of the conditional mean of functions depending on Y and other variables and where the response can follow other schemes of incomplete data (not only censored but also missing or length-biased data). For each procedure, asymptotic properties are established while finite sample behavior is studied via simulations. Examples from a variety of areas highlight the interest of using the proposed methodologies in practice.

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