Cyanobacteria contain both PSI and PSII. Their light-harvesting system is different from that found in plants (they use phycobilins, rather than chlorophylls, as antenna pigments), but their electron transport chain
           → PSII → plastoquinol → bf → cytochrome c → PSI → ferredoxin  →  NADPH
                                                  bf       ←     plastoquinol
is, in essence, the same as the electron transport chain in chloroplasts.  The mobile water-soluble electron carrier is cytochrome c in cyanobacteria, having been replaced by plastocyanin in plants.
Cyanobacteria can also synthesize ATP by oxidative phosphorylation, in the manner of other bacteria.  The electron transport chain is
            NADH dehydrogenase → plastoquinol → bf → cyt c → cyt aa → 
where the mobile electron carriers are plastoquinol and cytochrome c, while the proton pumps are NADH dehydrogenase, cyt bf and cytochrome aa (member of the COX3 family).
Cyanobacteria are the only bacteria that produce oxygen during photosynthesis. Earth's primordial atmosphere was anoxic. Organisms like cyanobacteria produced our present-day oxygen-containing atmosphere.
The other two major groups of photosynthetic bacteria, purple bacteria and green sulfur bacteria, contain only a single photosystem and do not produce oxygen.