Firstly: Dry Ablution for Minor Hadath
Dry ablution is legislated for removing minor hadath when there is no availability of water, or inability to use it. Consensus has been quoted over this by: Shams al-Deen Ibn Qudamah, al-Nawawi, and al-Shinqiti.
Secondly: Dry Ablution for Major Hadath
Dry ablution is legislated for removing major hadath like janabah, menstruation, and postnatal bleeding, if there is no availability of water, or inability to use it. This is by agreement of the four schools of jurisprudence.
Thirdly: Intercourse with One Who Lacks Water
Sexual intercourse is permissible for the ones upon purification from water but does not have availability to water. This is by agreement of the four schools of jurisprudence.  It is makruh for Malikis according to the relied upon opinion. It is also the position of the Zahiris and a group from the Salaf.
Fourthly: Ritual Washing for the Junub If He Finds Water
If someone who is junub prays with dry ablution, then finds water, then washing has become wajib for him. Consensus has been quoted on this by: Ibn `Abd al-Barr, al-Nawawi, and al-Shawkani.
Fifthly: Dry Ablution Out of Fear of Missing Jumu`ah Prayer
Dry ablution is not legislated for the one who fears missing the prayer if he performs normal ablution. This is by agreement of the four schools of jurisprudence.
Sixthly: Dry Ablution Out of Fear of Missing a Wajib Prayer
If a person fears missing the time for a wajib prayer due to ablution or washing, then he performs ablution or ritual washing regardless, then prays even if it is outside the time of validity. This is the position of the majority: Hanafis,  The rule for Hanafis in this matter: is that a person performs dry ablution for anything he fears missing and anything which has no replacement, like the funeral and Eid prayers, but not what he fears missing from voluntary prayer, nor what has an alternative like the five obligatory prayers and jumu`ah prayer. Shafi`is, Hanbalis, an opinion among Malikis, and the position of the majority of scholars.
Seventhly: Renewing Dry Ablution
It is not mustahabb to renew dry ablution, and this is by agreement of the four schools of jurisprudence.