Biology is dominated by transport problems involving fluid flows, from the transport of nutrients and locomotion to flows around plants and the circulatory system of animals. In this talk, I will discuss three instances of flows arising inside living cells. First I will present our work modelling natural cytoplasmic streaming in Drosophila embryo, an elongated multi-nucleated cell that is a classical model system for eukaryotic development and morphogenesis (https://doi.org/10.1098/rsif.2023.0428). I will next discuss our work on artificial cytoplasmic streaming, rationalising recent experiments that generate artificially induced intracellular flows using focused light localised inside individual cells (https://doi.org/10.1103/PhysRevFluids.8.034202). Finally, I will present work in progress addressing the controversial issue of natural convection flows inside cells arising from small temperature differences, and their impact on intracellular material transport.