The first generation: containers and compromises
TIFF (1986) came from the desktop publishing boom — a flexible tagged container that could hold almost anything, which is exactly why print and scanning still use it and why the files are enormous.
GIF (1987) was designed by CompuServe for dial-up: 256 colours, lossless LZW compression, and from the 1989 revision, animation. For flat graphics on a 1200-baud modem it was a good answer.
JPEG (1992) was the first format built specifically for photographs, and it got the hard part right immediately. Thirty years of successors have improved on it by 25–50% — meaningful, but not revolutionary. Nothing has replaced it.