The origin, composition and acceleration mechanism of high-energy cosmic rays (E > 10**15 eV) have been long-standing mysteries in astroparticle physics. Their resolution is by no means an easy task, as it implies to overcome several theoretical and experimental challenges. In spite of this, during the last decade considerable progress has been made as different instruments have provided us with several clues which have narrowed down the possible answers to the main questions in cosmic ray research. Some of these clues are related with key observations of the energy spectrum, composition and arrival direction of cosmic rays, which have been performed with unprecedented precision and statistics, and with multi-messenger observations of the high-energy sky provided by modern gamma-ray and neutrino telescopes. In addition, recent observations have provided unexpected results, which if they are confirmed, may point out that our previous conceptions of the high-energy cosmic-ray physics may be not as simple as previously thought. In this talk, I will present a brief overview of the current status of the experimental cosmic-ray research and will discuss some of the challenges that it faces with special emphasis on the role of the high-energy hadronic interaction models, which play an important part in the interpretation of the cosmic-ray data.