I have heard that in the Orthodox world rabbis that teach are referred to as "Rabbi" even though they might not have semicha. Even several roshei yeshivah might not have semicha. can this be true?
It depends what you mean by semicha -- there is a basic level of "being a rabbi" that is summarized here:
There is a new form of semicha which is circulating today, known as the "Rav Umanhig" semicha. This is essentially a semicha which does not necessarily vouch for the recipient's knowledge or competency in halacha, but rather, testifies that the recipient is worthy to be called "rabbi" and serve in a position of leadership. In some yeshivot there is a formal curriculum which must be completed before receiving this semicha, usually extensive sections of the Orach Chaim section of Shulchan Aruch. Other rabbis and yeshivot simply issue this semicha to students who are well rounded and have an impressive grasp of general Jewish scholarship and are therefore worthy of the title "rabbi". Indeed, it is important to recall that "rabbi" essentially means "teacher", not necessarily "halachic authority".
It is somewhat unclear how or why this semicha evolved. According to one theory, the Rav Umanhig semicha may have been first created by the Ner Yisrael yeshiva in Baltimore in order to allow yeshiva students to evade the draft during the Korean and Vietnam Wars under the "clergy" clause. After the draft was over, the Rav Umanhig semicha continued for those wishing to enter Jewish communal work, though not necessarily as pulpit rabbis. In this way those in teaching and similar positions could legitimately be addressed as "rabbi" without having to go through the intensity of formal semicha studies and learning the Yoreh Deah material.
So one could be, according to this, called "rabbi" simply as a function of their holding a particular teaching role but without the testing and approbation of forml semicha.**
It is important to understand that the Semicha of today is not "Traditional Semicha" which was only given in an unbroken chain from Moshe Rabbeinu down, from each teacher to their (worthy) students. That Semicha was lost long ago. (Although it is possible to bring back according to the Rambam, and was attempted by Rav Yaakov Beirav in 1538).
What, then, is the Semicha of today?
The Rema (Y.D. 242:14) writes that the Semicha of today is there for two purposes:
- For people to believe that he is capable of ruling on Halachic Shailot
- As permission from his teacher to rule. (As one is prohibited from issuing a Halachic ruling in the same city as his teacher without permission.) As such, if he lives in a different city, or his teacher is no longer alive, he would not need permission. As well, today most people do not have a רבו מובהק and therefore would not require permission.
Essentially, the only reason for most people to have Semicha today is for people to trust him. There is no Halachic requirement for someone to have Semicha in order to rule on a question to which he knows the answer.
Rabbi Gedalia Anemer,zt'l, used to bristle when a day school principal would have all male Jewish subject teachers referred to as "rabbi" whether or not they had earned the credential. There have been impressive yeshiva instructrs at institutions such as Ner Israel who (20 years ago) might just be "mister" so and so. Those days are disappearing, though and more and more Talmud instructrs without smicha are now called "rabbi" even though his working knowledge of the Shulchan Aruch may be limited.