Here are 10 economic challenges that Mr Modi faces
Goods and Services Tax (GST): India's most ambitious indirect tax reform would replace existing state and central levies with a uniform tax, boosting revenue collection while cutting business transaction costs. GST, which could boost India's economy by up to two percentage points, has so far faced resistance from various states, including those governed by the BJP who fear a loss of their fiscal powers. The BJP aims to address state concerns and implement GST in an "appropriate timeframe". The Congress party would back the reform in opposition, a senior party member told Reuters earlier this month. The reform needs broad backing because it requires a change in the constitution.
Central bank policies: A Reserve Bank of India panel in January proposed key changes including targeting consumer price inflation and making a committee responsible for monetary policy, and not the RBI Governor alone. This would require changes to the RBI Act. The BJP top brass has not spoken widely on the issue, but it will likely be a tough sell for RBI Governor Raghuram Rajan. He has the backing of some global agencies like the International Monetary Fund. Mr Modi's government may also look to eventually separate the debt management function from the RBI, on the grounds that debt management sometimes conflicts with the central bank's monetary policy stance.
Privatisation: The new government is likely to focus on selling its holdings in state-run firms that could raise much-needed revenues to trim India's ballooning fiscal deficit and boost economic growth. The rising stock market helped New Delhi raise more than $3 billion (Rs 18,000 crore at 60 rupees per dollar) via stake sales in the fiscal year to March 31 - but that was only a third of the government's original target. The outgoing government announced plans to raise Rs 56,900 crore through asset sales in 2014-15. This could help achieve a lower fiscal deficit target of 4.1 per cent of GDP. These estimates may be revised by the next government.
Subsidies: Mr Modi's government needs to examine how it subsidises basic commodities if it is to contain the fiscal deficit and avoid a ratings downgrade. Subsidies cost an estimated 2.2 per cent of India's GDP in 2013-14. The BJP in its manifesto said it will seek greater fiscal discipline without compromising on the availability of funds for development.
Labour: The BJP wants to reform labour laws to boost job-intensive manufacturing and create as many as 1 crore jobs a year for young Indians entering the workforce. Changing the law would be politically tricky, though, and Mr Modi may seek to encourage competition between India's states to boost job creation.
Defence: More foreign investment in defence would help India reduce imports, modernise weapons systems and speed up deliveries of hardware it needs for operations and training. India, the world's biggest arms importer, now allows 26 per cent foreign ownership in defence, and proposals to exceed that limit are considered only for state-of-the-art technology. The BJP has said it would allow some greater foreign investment in defence industries.
Insurance: Attempts to raise the cap on foreign investment in India's $45 billion (Rs 2.70 lakh crore) insurance sector, to 49 per cent from 26 per cent, have met resistance from employees at state-controlled insurers and their political backers. A BJP leader said in March the party had held talks with Congress to break the deadlock.
Banking: The next government will need to help state-run lenders battling rising bad loans caused by the slowing economy, rising interest rates and project delays. Stressed loans in India - either bad or restructured - total $100 billion (Rs 6 lakh crore), or about 10 per cent of all loans. Fitch Ratings expects that ratio to reach 14 per cent by March 2015. Rising bad loans threaten to choke the gradual recovery in Asia's third-largest economy, according to the OECD. The interim budget in February set aside Rs 11,200 crore to help the sector meet key capital ratios, but analysts say more money is needed.
Power: A BJP-led government may implement the so-called Gujarat model of distributing electricity that has been widely praised for delivering reliable 24-hour power supplies in the state. Mr Modi provided different power feeds to farmers, households, and companies instead of a uniform feed in his home state.
Gas pricing: In January, India notified the new gas pricing formula that could double the prices of locally produced gas from April 1, but the poll regulator stopped the government from raising the prices until the elections are over. Reliance Industries and its partners BP and Niko Resources last week issued a notice of arbitration to the government seeking implementation of higher gas prices. The BJP-led government may review the formula on the lines suggested by a senior party leader last year and announce the date of implementation of new prices.