The light-induced/dark-reversible changes in the chlorophyll (Chl) a fluorescence of photosynthetic cells and membranes in the mus-to-several min time window (fluorescence induction, FI; or Kautsky transient) reflect quantum yield changes (quenching/de-quenching) as well as changes in the number of Chls a in photosystem II (PS II; state transitions). Both relate to excitation trapping in PS II and the ensuing photosynthetic electron transport (PSET), and to secondary PSET effects, such as ion translocation across thylakoid membranes and filling or depletion of post-PS II and post-PS I pools of metabolites. In addition, high actinic light doses may depress Chl a fluorescence irreversibly (photoinhibitory lowering; q(I)). FI has been studied quite extensively in plants an algae (less so in cyanobacteria) as it affords a low resolution panoramic view of the photosynthesis process. Total FI comprises two transients, a fast initial (OPS; for Origin, Peak, Steady state) and a second slower transient (SMT; for Steady state, Maximum, Terminal state), whose details are characteristically different in eukaryotic (plants and algae) and prokaryotic (cyanobacteria) oxygenic photosynthetic organisms. In the former, maximal fluorescence output occurs at peak P, with peak M lying much lower or being absent, in which case the PSMT phases are replaced by a monotonous PT fluorescence decay. In contrast, in phycobilisome (PBS)-containing cyanobacteria maximal fluorescence occurs at M which lies much higher than peak P. It will be argued that this difference is caused by a fluorescence lowering trend (state 1 --> 2 transition) that dominates the FI pattern of plants and algae, and correspondingly by a fluorescence increasing trend (state 2 --> 1 transition) that dominates the FI of PBS-containing cyanobacteria. Characteristically, however, the FI pattern of the PBS-minus cyanobacterium Acaryochloris marina resembles the FI patterns of algae and plants and not of the PBS-containing cyanobacteria.