Moments of random multiplicative functions, III: A short review

We give a short review of recent progress on determining the order of magnitude of moments $\mathbb{E}\mathrm{\mid }{\sum }_{n\le x}f(n){\mathrm{\mid }}^{2q}$ of random multiplicative functions, and of closely related issues. We hope this can serve as a concise introduction to some of the ideas involved, for those who may not have too much background in the area.