Often real networks are not fully observed, either because of limited experimental capacity to collect the information or because of the magnitude of the system's size. Similarly, data collection can be noisy, as when edges are mistakenly reported or when their magnitude is not clear enough. This leads on one hand to the challenge of estimating hidden parameters, labels, community memberships or centrality measures from an observed dataset subsampled from some larger and noisy network. On the other hand, given the biasing effect of how the network information was collected, an open challenge is to develop theoretical ideas into feasible data collection algorithms that are capable of correcting for these effects.