Before 1911, when the capital was Calcutta (now Kolkata), Delhi was a part of the Punjab province. It was made the capital in 1911, to be governed by a Chief Commissioner.
Not really. There was of lack of coordination between various central government departments in knowing and resolving the needs of the people of Delhi. This led to the constitution of Sitaramayya Committee in 1947. The committee recommended Delhi to function under a Lieutenant Governor appointed by the President. The LG would act on the advice of the Centre.
Post-independence, Delhi was made a type C state to be governed under the Chief Commissioner. Delhi's state assembly came into existence in 1952, with Chief minister Chaudhary Brahm Prakash and the council of ministers to advise the commissioner. The Chief Minister then did not have powers on police, land, sanitation and municipal authorities.
The assembly and chief minister post were scrapped with the enactment of State Reorganization Act, 1956, and Delhi was made a Union Territory under the direct administration of the President of India. Subsequently, the Municipal Corporation was formed in Delhi.
In 1966, the assembly was replaced by Delhi Metropolitan Council with 56 elected and five nominated members. The council had no legislative powers, only an advisory role to the LG, who was at the helm of the administration.
Article 239AA was introduced. Delhi was constitutionally given the title of “National Capital Territory of Delhi” that would be administered by an LG. The LG would be appointed by the President and a Legislative Assembly was to be constituted. A council of Ministers to advise the LG were to be formed. The LG was not bound to consult the council of ministers only in cases related to land, police and public order.
The Arvind Kejriwal government, since the time it has been elected, has been at loggerheads with the LG over a number of issues related to governance. The Delhi HC had ruled against Delhi government and said that Delhi was a Union Territory and the LG was not bound to act on the aid and advice of the Delhi Legislative Assembly. This was challenged in the Supreme Court by the Delhi government. The Supreme Court in its verdict has held now Lieutenant Governor does not have independent decision-making powers and is bound to act on the aid and advice of the Council of Ministers.