High-energy cosmic neutrino puzzle: a review

We appraise the status of high-energy neutrino astronomy and summarize the observations that define the 'IceCube puzzle.' The observations are closing in on the source candidates that may contribute to the observation. We highlight the potential of multi-messenger analysis to assist in the identification of the sources. We also give a brief overview of future search strategies that include the realistic possibility of constructing a next-generation detector larger by one order of magnitude in volume. (review)