This article describes an emerging method for quantitative measurement and spatial imaging of microviscosity within individual domains of live cells. The method is based on fluorescence detection from small synthetic molecules termed 'molecular rotors', which are characterised by a strong response of fluorescence lifetimes or spectra to the viscosity of their immediate environment. Alongside this new method, two complementary techniques are discussed, which provide further insights into diffusion controlled processes on a microscopic scale in a biological environment. These are time resolved fluorescence anisotropy and imaging of short-lived excited state of molecular oxygen, termed 'singlet oxygen'. It is possible to utilise all three approaches for the quantitative determination of viscosity in individual organelles of live cells. Finally, it is discussed how the major advantage of molecular rotor imaging, fast signal acquisition, can be used to monitor changing viscosity during dynamic biological processes within cells, such as photoinduced cell death.