In this talk we introduce synthesis of infinite-dimensional observers for infinitedimensional systems described by C0 semigroups. We study specifically the situation where only boundary measurement is available. Infinite-dimensional Luenbergerlike observers are proposed in the abstract framework of semigroup systems. Exponential convergence of the designed observers is proved in the abstract framework by using Lyapunov techniques. For examples explicit observers are worked out to PDE systems such as Euler-Bernoulli elastic beam and water wave systems. Thanks to observability property exponential or strong convergence of the designed observers is established along with convergence rate estimated in terms of the system parameters, which is a desirable property for practical applications.