All Praise be to Allah and all blessings be on the Prophetﷺ.
Ijarah in the Shariah is very important because it deals with many conventional trade practices in today’s society. Ijarah means providing services and goods temporarily for a wage or a reimbursement. 
In terms of Islamic banking system it means that the bank will purchase the asset and lease out to the customer for an agreed rental fee. This agreement will not include a promise to buy the asset at the end of the term of the agreement since this is pure renting.
It is different from the Conventional leasing system, because it does not contain any condition which contradicts the Shariah. All risks of ownership are borne by the Lessor while all risks pertaining to normal usage are based by the lessee in Ijarah system while in conventional banking; all risks are with the customer. Moreove
r the lessor cannot charge any interest on delayed payment since it is a form of a prohibited transaction. 
Ijarah is generally divided into two kinds: Operating lease and Rental Purchases. Operating lease is a kind of renting in which the asset returns to the lessor after the period of lease has been completed and after that the lessor then looks for a new lessee to lease out the asset. All the risks of ownership, recession, etc remains with the lessor.
There is also a third type of leasing which is known as forward lease or Ijara Mawsoofa bil thimma. This lease is executed at a future date. This type of leasing or Ijarah is generally a combination of construction finance and a redeemable leasing agreement.
While Rental Purchases or ‘ Ijarah muntahiya ila tamleek’ is a way in which the customer has an option to purchase the asset at the end of the term. It is similar to Ijarah in the sense that the asset is leased/rented out but the difference comes when the option is given to the lessee to purchase the asset at the end. When the last installment is paid, the lessee can have exercise three options that is he could either renew the contract, terminate the contract or he could purchase the asset. 
It is permissible in the Islamic Shariah as long as the rental contract is accompanied by a separate and independent contract giving the asset to the lessee as long as he pays of all the rent. This is also unanimously agreed by the Fiqh Council.
However this type of contract is not a mixed contract which is known as “Rent to Own”. In this type of contract, there is a combination of two types of contracts, where the lessee keeps paying rent and then when the last rental amount is given, the asset becomes his. This type of transaction according the Council of Senior scholars is prohibited since it is neither a sale nor is it a purely rental service. The purchaser or the lessee cannot sell the asset until the last installment is paid and if he fails to do so, the lessor can take the asset back and the money is not given back. In this case the lease contract automatically changes into a sale contract and the only consideration which is paid is the rent. Hence it is clear that this type of contract is totally different from Rental Purchases and this type of Rent to own contract is prohibited.
Another one which is prohibited is a transaction where the lease agreement itself contains an option to purchase the asset. Since this condition is included in the contract itself and no separate and independent contract was signed, this form also becomes prohibited.
The Lessor in an Ijarah transaction is called as the Mu’jir , while the Lessee is called as the Musta’jir and the rent is called as the Ujrah. If the deal involves agreeing to two different contracts for the same commodity for the same duration, at the same time then it becomes a form of a prohibited contract. It should be totally an independent contract. The sale contract succeeds the lease contract and the lease contract should be a bona fide contract and not just a farce or a veil to hide a sale transaction.
Moreover, all the costs of the ownership are borne by the lessor since he owns the asset while all the costs relating to the operations and the maintenance is borne by the lessee. All the Shariah rulings are applicable to Ijarah and all the shariah rulings relating to sale will be applicable when the asset is sold to the lessee.
Another contract which is an independent contract stating that the asset will go as a gift to the lessee is permissible since it is not embedded in the leasing contract and is separate from it. This type of gift will only be applicable once the lease period has been completed and when the lease or rental payments have been paid by the lessee. 
In Modern Islamic banks, the leasing contract is the major contract which follows all the Shariah conditions relating to Ijarah. The bank can also take an earnest money for making sure that the person is indeed serious in leasing the asset and this amount is kept by the bank as a trust. The other contract is the subsequent sale, promise to gift or promise to a contingent gift which comes under the Rental Purchases. The bank can also take a Tafakul cover or an Insurance cover of the asset under the Shariah conditions and in case of default, the amount received over and above the bank’s costs and expenses goes to the client. 
Hence there are several conditions which make the Rental Purchases permissible as the Prophet ﷺ said “The Muslims are bound by their (agreed) conditions except the condition that permits what is forbidden or forbids what is permissible.”
One must be very careful to not enter into a prohibited transaction and make sure that all the terms and conditions are Shariah compliant, since many a times the conventional hire purchase system is simply renamed as Ijarah Muntihiyah bi Tamleek and they do not follow any conditions of the Shariah. In this way they easily deceive the innocent lessee and causing him to enter into a prohibited transaction.
And Allah Knows best.
 6 Abu Daud, Sunan Abi Daud, Bait al-Afkar al-Dawliyyah, 1999, p. 398, hadith no. 3594.