Representations of the fundamental group of an orientable surface of finite type into a Hermitian Lie group G with maximal Toledo invariant are of particular interest in the higher Teichmüller theory. These representations were studied by M. Burger, A. Iozzi, and A. Wienhard and generalize Fuchsian representations of the fundamental group of a surface into PSL(2,R). Moreover, maximal representations have particularly nice properties, e.g. they are injective with a discrete image in G. In my talk, I introduce the X-type coordinates on the decorated space of maximal representations of the fundamental group of a punctured surface into Sp(2n,R). These coordinates generalize the Fock-Goncharov coordinates for representations into PSL(2,R). If time permits, I will talk about how we can understand the topology of the decorated space of maximal representations using these coordinates. This is a joint work with D. Alessandrini, O. Guichard and A. Wienhard.