This chapter addresses some of the challenges associated with trying to model population fluctuations, bloom formation and collapse of planktonic cyanobacteria. It is argued that improved modelling and prediction rely on a better understanding of the physiological responses of cyanobacteria to the physical and chemical characteristics of their environment. In addition there is a need to better understand the complex trophic interactions that influence population dynamics. The high variability of cyanobacterial populations represents a major challenge for models attempting to make predictions at the whole lake scale. Many of the physiological attributes described within specific models do not capture the dynamics of cyanobacteria, because of the extensive parameterisations required by the array of descriptive algorithms. The physiological attributes to be modelled include the ability to fix nitrogen, storages of both nitrogen and phosphorus, capture light across a range of wavelengths with specific accessory pigments, form colonies or filaments, and regulate buoyancy through the balance between gas vacuoles and cellular constituents. Recruitment of populations from sediments may also be important in bloom formation, but is not considered in this chapter. Although there is a commonality in models of cyanobacteria and micro-algae with their descriptions of photosynthesis, nutrient uptake, movement and grazing, there is a need to differentiate the cyanobacteria based on their key attributes, if their occurrence and succession are to be predicted separately from the micro-algae. The challenge is to develop models that incorporate complex physiological processes, responsive to changes at a range of ecosystem scales, but without excessive calibration of the key underlying algorithms. One suggestion is to turn from the single limiting-factor modelling approach that creates a plethora of disjointed algorithms and develop bio-mechanistic representations of integrated cellular function that incorporate dynamic responses to ...