In Mormonism, Prophets in biblical and Book of Mormon times would preach unto the people to repent. What they did, which was preach unto the people, heal the sick and afflicted, and bless those who are righteous. Well know missionaries in the bible include the Apostles of Jesus, John the Baptist, and Paul of Tarsus. They worked hard, not only just preaching the gospel, but they helped those in need. They cared about people. Paul for example, traveled from Jerusalem around the Mediterranean Sea three times, preaching to thousands of people, performing many miracles, jailed and escaped multiple times, he is a prime example of what a missionary does.
There are missionaries today as well as in biblical times. The Church of Jesus Christ of Latter-day Saints has around 65,000 to 70,000 missionaries today, sent to all parts of the world. There are quite a few countries that will not allow missionaries to preach, mainly the middle east (Turkey, Iran, Iraq, UAE, Saudi Arabia, Israel, Syria) for both religious reasons, and safety reasons. There are a few countries in other areas that won't allow missionaries due mainly to safety reasons but sometimes as religious reasons as well.
Just this year, the First Presidency of the Church announced that the set age to go on a mission went from 19 years old to 18 years old. This was well received and many youth were excited to spread the word. Age is not the only thing that restricts someone to go on a mission, the standards set by the First Presidency mainly include being worthy of serving a mission. That includes confessing to any serious sins you have committed, including breaking the Word of Wisdom and the Law of Chastity. They set standards so that they have as many youth strong in the spirit as possible. It allows those who really have it in their hearts to spread the gospel and baptize those who want to become members of the church. There are many testimonies that I have alone heard, including my father, talking about how going on a mission was the best thing that they ever did.