Trivalent neodymium ion (Nd3+) doped materials cover the spectral range of 0.9~1.4 μm. Based on Nd3+ doping, numerous laser materials have been developed. Near 0.9 μm band, frequency multiplier technology can convert the laser into blue light, which is used in display technology and biomedical imaging; near 1.06 μm band, the laser output belongs to a four-level system with high gain, making it easy to achieve high-power output, and being used for industrial laser cutting and laser surgery, and so on; near 1.4 μm band, it benefits from eye-safe properties, atmospheric transmission characteristics, gaining wide applications in high-precision lidar, biomedical applications and fine processing. Studies about infrared laser sources have been widely recognized over the past few decades due to their various potential applications. This review provides a detailed introduction to the pulsed laser performance of Nd3+-doped laser crystals in oxide and fluoride matrices. It also analyzes the nonlinear optical properties and application ranges of traditional saturable absorbers and emerging two-dimensional saturable absorbers. Finally, it summarizes the current research status and development trends of passive Q-switched Nd3+-doped solid-state lasers in relation to substrates and saturable absorbers and resonant cavities. We believe that this review will provide a deeper understanding of passive Q-switching Nd3+ solid lasers.