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New and forthcoming deep-wide surveys, from instruments like the HSC, LSST and EUCLID, are poised to revolutionize our understanding of galaxy evolution, by revealing aspects of galaxies that are largely invisible in past wide-area datasets. These surveys will open up the realm of low-surface-brightness (LSB) and dwarf galaxies -- which dominate the galaxy number density -- for the first time at cosmological distances. They will also reveal key, unexplored LSB structures which strongly constrain our structure-formation paradigm, such as merger-induced tidal features and intra-cluster light. However, exploitation of these revolutionary new datasets will require us to address several data-analysis challenges. Data-processing pipelines will have to preserve LSB structures, which are susceptible to sky over-subtraction. Analysis of the prodigious data volumes will require machine-learning (in particular unsupervised techniques), to augment or even replace traditional methods. Cosmological simulations, which are essential for a statistical understanding of the physics of galaxy evolution, will require mass and spatial resolutions that are high enough to resolve LSB/dwarf galaxies and LSB structures. And finally, estimation of physical properties (e.g. stellar masses and star formation rates) will require reliable redshift information. Since it is unlikely that even next-generation spectrographs will provide complete spectral coverage in the LSB/dwarf regime outside the nearby Universe, photometric redshifts may drive the science from these datasets. It is necessary, therefore, that the accuracy of these redshifts is good enough (e.g. < 10 per cent) to enable statistical studies in the LSB/dwarf regime. I outline the tremendous discovery potential of new/forthcoming deep-wide surveys and describe techniques which will enable us to solve the data-analysis challenges outlined above. (Abridged)