Cyanobacteria carry out oxygenic photosynthesis, play a key role in the cycling of carbon and nitrogen in the biosphere, and have had a large impact on the evolution of life and the Earth itself. Many cyanobacterial strains exhibit a multicellular lifestyle, growing as filaments that can be hundreds of cells long and endowed with intercellular communication. Furthermore, under depletion of combined nitrogen, filament growth requires the activity of two interdependent cell types: vegetative cells that fix CO2 and heterocysts that fix N2. Intercellular molecular transfer is essential for signaling involved in the regulation of heterocyst differentiation and for reciprocal nutrition of heterocysts and vegetative cells. Here we review various aspects of multicellularity in cyanobacterial filaments and their differentiation, including filament architecture with emphasis on the structures used for intercellular communication; we survey theoretical models that have been put forward to understand heterocyst patterning and discuss the factors that need to be considered for these models to reflect the biological entity; and finally, since cell division in filamentous cyanobacteria has the peculiarity of producing linked instead of independent cells, we review distinct aspects of cell division in these organisms.