These days, with the advancement of digital photography, the use of supplemental camera lighting for most applications is of minor concern. However the early photographers were faced with much longer times taken to capture an image and so adequate lighting was a much bigger issue.
Many early photographers constructed special rooms with large windows and many reflectors to maximize the light falling on their subject. The development in Manchester in 1863 of the manufacture of magnesium was an early breakthrough and allowed experimenters in the following year to successfully take a photograph in the Blue John Mine Derbyshire by igniting magnesium.
Using an open pan of magnesium was inherently dangerous. The famous C19 photographer Jacob Riis, for example set fire to his house twice and himself once, so the development of glass bulbs to contain magnesium wire in oxygen during the 1930s was a very big step forward. The development of the flashgun followed, but the guns had to be synchronised to the shutter action of the camera.
Camera makers generally had flash guns designed to fit their own cameras, either from specialists or in-house. Kodak in particular eventually produced a wide range of flash guns but many were only usable on their specific models. Eventually the demand for universally usable flash guns developed as mounting shoes and standard connectors became common. The guns required a reflector for best results, but this made them bulky, so folding interleaf reflectors or folding down reflectors soon followed on. Flash bulbs were gradually reduced in size, bulbs becoming capless during the 1950s and batteries were phased out. Smallness became important. The most compact design was the Tully.
Electronic flash guns were introduced in the 1960s and took over from bulb guns. Eventually the bulbs were abandoned and flash cubes came in. Kodak was at the forefront especially on their Instamatic range. These provided 4 flashes per cube and could be used with a tall fitting for best photographic results. Progress in electronics from the 1960s onward allowed the introduction of built-in flash which eventually became the norm for almost all but the cheapest cameras.