Cosmic rays are the only sample of matter coming from outer space. They carry rich information about particle physics, high-energy astrophysics, composition and evolution of the Universe. The highest energy of cosmic rays detected so far is about 3×10 20 eV. How are the cosmic rays accelerated?What kind of astronomic sources do the cosmic rays originate from?Are the fundamental physics laws still valid in such high-energy scales? are all important scientific problems waiting to be addressed. To answer these questions, various space and ground experiments have been carried out to explore the nature of cosmic rays in a multi-messenger approach. The past few decades have witnessed great achievements in high-energy cosmic ray, gamma ray, neutrino observations, and detection of gravitational wave. (1) The cosmic ray spectra, composition, and anisotropy have been measured with unprecedented precision leading to better understanding of cosmic ray acceleration and transport and stricter constraints on properties of potential candidates of dark matter particles, and the dipole anisotropy of ultrahigh energy cosmic rays indicates that they have an extragalactic origin. (2) Space borne experiments have discovered more than 3000 sources in the GeV range, and the ground based experiments have uncovered more than 200 sources at TeV energies. Most of these sources are high-energy electron accelerators, and a few of them are identified as the accelerators of cosmic ray nuclei. Diffuse gamma-ray emission associated with galactic disks and jets and/or outbursts of Active Galactic Nuclei is also measured with better spatial and energy resolutions, which can be used to study cosmic ray transport in the interstellar/galactic/cluster medium. (3) With the IceCube experiment, about 100 high-energy neutrino events have been recorded and their isotropic distribution suggests an extragalactic origin. (4) The first gravitational wave event with simultaneous multi-wavelength observations has been detected opening the epoch of gravitational wave astronomy. Strong gravitational wave events represent the most catastrophic energy release in the Universe and can be important cosmic ray sources. These new results established the foundation to address the origin of cosmic rays and to develop theories of particle acceleration and transport. The study of cosmic ray transport has gone beyond the diffusion approximation to study the effect of magnetic field fluctuations on small scale anisotropy of cosmic rays and comprehensive numerical modelings of cosmic ray transport in the Galaxy are advanced with multi-wavelength observations. Diffusive particle acceleration by strong shocks of supernova remnants (SNRs) is also advanced based on multi-wavelength observations and cosmic ray measurements. The scenario of SNR origin of Galactic cosmic rays is being quantified with testable predictions. Although there are still uncertainties in amplification of magnetic field by cosmic rays and cosmic ray scattering by turbulent plasmas, sophisticated numerical codes are being developed to address these issues. Successful construction and operation of new generation cosmic ray and gamma-ray experiments will open a new chapter of the astro-particle physics study.