The Act was formally titled the Succession to the Crown Act 1533 (citation 25 Henry VIII. c. 22), or the Act of Succession 1533; it is often dated as 1534, as it was passed in that calendar year. However, the legal calendar in use at that time dated the beginning of the year as March 25th, and so considered the Act as being in 1533.
The Act made Princess Elizabeth, daughter of Anne Boleyn, the true successor to the Crown by declaring Princess Mary, daughter of Catherine of Aragon, a bastard. The Act also required all subjects, if commanded, to swear an oath to recognise this Act as well as the King's supremacy. Any one who refused to take an oath was subject to a charge of treason. This is what happened to Sir Thomas More, who refused to swear the oath because it acknowledged the anti-Papal powers of Parliament in matters of religion.
The currently applicable legislation is the Act of Settlement 1701.