The problem of synchronization of chaotic systems in presence of additive bounded noise is considered. Three approaches to design of adaptive synchronization algorithms are presented: passification; identification with implicit signal model; identification with frequency modulation. Two ways of robustification of adaptation algorithms are studied: parametric feedback and the dead zone. Application of the proposed adaptive synchronization algorithms to the problem of signal transmission is discussed. The results are illustrated by numerical examples of information transmission with chaotic Chua system.