The time jitter of a femtosecond laser is the short-term deviation of the optical pulse position relative to its ideal equally spaced pulse position. Femtosecond lasers emit uniformly spaced ultrashort pulse train. The quantum-noise-limited timing jitter can be as low as few tens of attoseconds in millisecond time scale. This unique property and its advanced applications constitute a new branch of ultrafast research, "Attosecond precision ultrafast photonics". In this paper, the recent advances in femtosecond laser timing jitter research, high-precision timing jitter characterization methods, and the ultralow timing jitter that can be achieved by different kinds of femtosecond laser sources were reviewed. Finally, the application of low-jitter femtosecond lasers in the fields of synchronization of large-scale scientific instruments, high-speed analog-to-digital conversion, absolute ranging technology and coherent beam combination are introduced.