While Fuji is still a significant player in the bike business, there is not that much left of its Japanese heritage and origin anymore. Today, it is hardly anything else than a brand name in the portfolio of a Taiwan-based mass-market manufacturer.
The company was founded as Nichibei Fuji in Japan in 1899. It started with its own bike production in the 1920s, serving Japan and Asian neighbor states. A highlight were the 1964 Olympics, on which occasion Fuji designed the bikes for the Japanese national team. When in the 1970s Fuji established its US subsidiary, it was the first bike importer from Japan selling its products under its own name. With the bike boom, Fuji quickly became a household name in North America.
In the mid-80s, international currency realignments made Japan-made products disproportionately expensive in many export markets. Unfortunately, Fuji was among the last ones to address this by shifting its production to lower-wage neighbor states. In addition, the company focused for too long on its traditional range of road/touring bicycles, missing out on the mountain bike trend.
By the end of the 1990s, Fuji declared bankruptcy. It ended up getting acquired by US- and Taiwan-based investment companies, becoming a part of their portfolios of bicycle brands.
See the Classic Fuji web site for its line-up from its glory days.