The philosophy behind Islamic saving and investing can be traced to the Quran and other early Islamic texts. The story of the prophet Yusuf (Joseph, the same one as in the Bible) conserving grain from rich harvests in Egypt, related in Sura (chapter) 12 of the Quran, is often cited as an admonition to save against hard times. Other verses advise against squandering wealth, while the Prophet Muhammad warned in a hadith (a collection of his sayings) that one “who is prudent in spending will not be dependent on others” later in life.

Both the Quran and hadith inform Shariah, which guides Muslims through practical life decisions, including how they should make and save money while remaining true to their religious principles.

“Because Islam tends not to distinguish between the temporal and the religious, there is a perennial desire among Muslims to live all aspects of their lives, including the financial, in a manner consistent with their faith,” observed Usman Hayat and Adeel Malik, the authors of a 2014 study of Islamic finance by the CFA Institute.

The Accounting and Auditing Organization for Islamic Financial Institutions, Malaysia’s Islamic Financial Services Board and Bahrain’s International Islamic Financial Market are among the major independent organizations that help Muslims achieve these goals. Advised by boards of Islamic financial experts and religious scholars, these organizations continually and systematically review companies, bonds and mutual funds to ensure they are Shariah-compliant. The vetted products are listed on various Islamic indexes that have concurrently emerged.

“As Islamic funds were being developed, there was a need for benchmarks, and so we were responding to the needs of the assets management industry,” said Michael Orzano, the head of equity indices at S&P’s Dow Jones Indices. The original Dow Jones Islamic Market Index was introduced in 1999 as the world’s first Shariah-compliant index. Today, the company’s portfolio of more than 15,000 indexes is among many offered by major financial firms.

Like Shariah itself, which varies in interpretation (known as ijtihad), the indexes differ on what is compliant and what is not. Most regard the trade and manufacture of weapons as noncompliant, for example, yet S&P’s board of Islamic scholars takes a nuanced approach. The use of weapons can be permissible (self-defense) or nonpermissible (unprovoked violence), but the weapons themselves are neutral, so investing in their manufacture is sanctioned, as Mr. Orzano noted in a 2013 report.

A vast range of customized, equally nuanced Islamic financial products structured like standard investments but operating within Shariah has likewise gained traction in the market.