We analyze networks generated by the recurrence plots of the time series of chaotic systems and study their properties, evolution and robustness against several types of attacks. Evolving recurrence networks obtained from chaotic systems display interesting features from the point of view of robustness (in particular, those related to their connectivity), which could help in the design of systems with high capability and robustness for information diffusion. The approach is extended to cases where the equations of the chaotic system are not given (but are defined by their time series) using state-space reconstruction methods and we note that the general characteristics of the attractors generated by such systems are maintained under this transformation. A comparison with well-known complex network models is performed to illustrate the differences and similarities.