Challenges for Lambda-CDM and MOND

The Universe on large scales is well described by the Lambda-CDM cosmological model. There however remain some heavy clouds on our global understanding, especially on galaxy scales, which we review here. While some of these clouds might perhaps disappear through small compensatory adjustments of the model, such as changing the mass of the dark matter particles or accounting better for baryonic physics, others should rather be taken as strong indications that the physics of the dark sector is, at the very least, much richer and complex than currently assumed, and that our understanding of gravity and dynamics might also be at play. For instance, the empirically well-tested MOND phenomenology in galaxies, whatever its final explanation, should be understood in any model of galaxy formation and dynamics. Current alternatives to Lambda-CDM however bring with them many unsolved questions and challenges.