All EGMO problems (and solutions) from 2012 to 2021 can be found at https://www.egmo.org/, under “Past and future EGMOs”. For example, last years’s problems are available at https://www.egmo.org/egmos/egmo10/, in various languages.
We also recommend the blog of EGMO 2018 (organized in Florence, Italy), where you can find the detailed solutions and the arguments behind the solution of several EGMO problems in geometry, number theory etc.
EGMO problems are sometimes closely connected to real-world applications of mathematics. For example, Problem 6 from EGMO 2013 is closely related to coding theory, which we use in some form every day when our messages are sent to others after being transformed to 0-1 bits. In this article, former EGMO contestant Zsuzsanna Baran explains this connection, and the trade-off between the length of the messages and their stability, which is also important when we want to make sure that we can decode the message even if a few bits can change during the communication process.