What teachings of the Catholic Church have been formally defined as infallible?

The Church’s understanding of infallibility is often misunderstood. Many people wrongly believe that every word that comes from the mouth of the Pope is to be considered without error, completely true and therefore must be believed by every Catholic. This simply is not true. There are strict criteria governing how a teaching is made infallible and not all of them need the Pope’s formal consent. Tests for whether a definition of a teaching has been made infallible include: (a) if a pope is writing, does he use the phrase “define” and (b) if a church council is writing, does it use the phrase “let him be anathema” (the word anathema is this case means “outside of communion with Christ and the Church”). If either of these is the case, it’s probably an infallible definition, especially as this language has been used in recent centuries. There are other ways popes and councils can issue definitions, but these are phrases commonly used to do so. The Church has not yet compiled a list of all infallible teachings. However, the most common infallibly defined teachings are: the Immaculate Conception, the Assumption, the reservation of priestly ordination to men, abortion and the deliberate killing of innocent persons. Some of them—the Immaculate Conception and the Assumption—have been infallibly taught by a definition of the extraordinary magisterium (i.e., in a definition of a pope or an ecumenical council). Others—the male priesthood, the intrinsic evil of abortion and the deliberate killing of innocents—are infallibly taught, without a definition, by the Church’s ordinary magisterium (i.e., upheld in the Sacred Tradition by bishops and lay faithful). While the vast majority of what the Pope and Church councils say in spoken word and in writing are not considered infallible, this does not discount their truth or their relevance for our lives. It simply means they have not made a solemn pronouncement on the topic.