In the first part of this Chapter the present state of knowledge from the observations of cosmic rays between 10 ¹³ and 10 ²⁰ eV is summarized. This is not intended to be a complete review, but rather a broad overview of the relevant processes involving cosmic rays, including the astrophysical environments in which they take place. This overview mainly concerns experimental results and phenomenological aspects of their interpretation, therefore experiments’ description is not given but references to the vast bibliography are provided in the text. Some attempt is made to address the most popular explanations offered by theoretical models. The second part is devoted to the description of the LHAASO performance and of its capability to provide a response to several open questions, still unanswered, concerning cosmic rays above 10 ¹³ eV, highlighting which major steps forward in this field could be taken from LHAASO observations.