  We review the study of rogue waves and related instabilities in optical and
oceanic environments, with particular focus on recent experimental
developments. In optics, we emphasize results arising from the use of real-time
measurement techniques, whilst in oceanography we consider insights obtained
from analysis of real-world ocean wave data and controlled experiments in wave
tanks. Although significant progress in understanding rogue waves has been made
based on an analogy between wave dynamics in optics and hydrodynamics, these
comparisons have predominantly focused on one-dimensional nonlinear propagation
scenarios. As a result, there remains significant debate about the dominant
physical mechanisms driving the generation of ocean rogue waves in the complex
environment of the open sea. Here, we review state-of-the-art of rogue wave
studies in optics and hydrodynamics, aiming to clearly identify similarities
and differences between the results obtained in the two fields. In
hydrodynamics, we take care to review results that support both nonlinear and
linear interpretations of ocean rogue wave formation, and in optics, we also
summarise results from an emerging area of research applying the measurement
techniques developed for the study of rogue waves to dissipative soliton
systems. We conclude with a discussion of important future research directions.
