In recent years, with the development of laser technology, various non-diffraction beams each with a central spot unchanged after a long distance propagation, have been generated, they being the Bessel beam, higher Bessel beam, Mathieu beam, higher Mathieu beam, cosine beam, parabolic beam, and Airy beam. Diffraction-free beams are widely used in laser drilling, laser precision alignment, optical precision control, optical micromanipulation, optical communication, plasma guidance, light bullet, synthesis of autofocusing beam, nonlinear optics, etc. In this paper, the expressions, generation methods and corresponding experimental results of the various non-diffraction beams are presented. There are many ways to generate the Bessel beam, they being circular slit, computed hologram, spherical aberration lens, resonant cavity, axicon, and metasurface. The main methods of generating the non-diffraction beams are summarized, and each method is analyzed in depth from the cost of the system, and then some suggestions for improving and perfecting are made. For the generation of non-diffraction beams, the passive methods are used most to convert other beams into corresponding non-diffraction beams by optical components. Due to the low damage threshold and high cost of optical components, the power, energy and beam quality of a non-diffracting beam will be limited. How to generate a high-power, high-beam quality non-diffracting beam will be a hot research spot. Diffractionless beams have attracted a great deal of interest due to their unique non-diffraction, transverse-accelerating (or self-bending) and self-healing property. Transverse-accelerating property refers to that non-diffraction beams propagate along a parabola trajectory. The diffractionless beams' propagation trajectory control method implemented by changing system parameters is simple and easily successful, but cannot reverse acceleration direction, and its controlling range is limited. The self-healing property means that the non-diffraction beam tends to reform during propagation in spite of severe perturbations imposed. Both the Airy beam and the Bessel beam exhibit self-healing properties during propagation. And non-diffraction beams have potential applications in many fields. In atmosphere, such as in optical communication, non-diffracting beam exhibits more resilience against perturbations. Finally, brief summary and outlook of non-diffraction beams playing important roles in future study, and their application prospects are presented. In addition to Airy beam and Bessel beam, for other non-diffraction beams due to the complexity of the beams themselves, by comparison, their applications are investigated very little, so the applications in Mathieu beam, cosine beam, and parabolic beam will be a hot research spot.