What are Huddud crimes?
Hudud (also transliterated hadud, hudood; singular hadd, liter
al meaning "limit", or "restriction") is the word often used in Islamic literature for the bounds of acceptable behaviour and the punishments for serious crimes. In Islamic law or Sharia, hudud usually refers to the class of punishments that are fixed for certain crimes that are considered to be "claims of God." They include theft, fornication, consumption of alcohol, and apostasy.
Hudud offenses are defined as "claims of God," and therefore the sovereign was held to have a responsibility to punish them. All other offenses were defined as "claims of [His] servants," and responsibility for prosecution rested on the victim. This includes murder, which was treated as a private dispute between the murderer and the victim's heirs. The heirs had the right to compensation and to demand execution of the murderer (see qisas), but they could also choose to forgive.
- Theft (sariqa,)
- Highway robbery (qat' al-tariq,)
- Illegal sexual intercourse (zina')
- False accusation of zina' (qadhf,) 
- Drinking alcohol (sharb al-khamr)(Unlike the first four offences listed above , not all jurists consider drinking alcohol to be a hudud offense.)
- Apostasy ( ridda,) includes blasphemy. (Unlike the first four offenses listed above, not all jurists consider apostasy to be a hudud offense.)
What are punishments for Huddud crimes?
The punishments vary according to the status of the offender - Muslims generally receive harsher punishments than non-Muslims, free people receive harsher punishments than slaves, and in the case of zina', married people receive harsher punishments than unmarried.
In brief, the punishments include:
- Capital punishments - by sword/crucifixion (for highway robbery with homicide), by stoning (for zina' when the offenders are mature, married Muslims)
- Amputation of hands or feet (for theft and highway robbery without homicide)
- Flogging with a varying number of strokes (for drinking, zina' when the offenders are unmarried or not Muslims, and false accusations of zina')
What are Tazir crimes?
In Islamic Law, tazir (or ta'zir, Arabic) refers to punishment, usually corporal, that can be administered at the discretion of the judge, as opposed to the hudud (singular: hadd), the punishments for certain offenses that are fixed by the Qur'an or Hadith. Traditionally, ta'zir punishments could be applied to offenses for which no punishment is specified in the Qur'an. They could also be applied to hadd offenses in situations where the standards of proof required for hudud punishments could not be met.