Bloomberg Markets Magazine has published an in-depth investigation into business practices at Koch Industries, run by politically influential brothers Charles and David Koch. The story lays out what it suggests is a decades-long pattern of illegal and unethical behavior at Koch.

Both Bloomberg Markets Magazine's story and Koch's official response are long and full of complicated details, and it's not easy to untangle it all. Here's our guide to what seem to be the newest, most significant allegations.

Undisputed: Koch's subsidiaries in Europe got contracts through bribes in at least six countries.

In 2008, in the wake of a $1.6 billion settlement by the German engineering giant Siemens for bribing officials around the world, Koch conducted an internal investigation of its own payment practices. The company found that Koch-Glitsch France had paid illegal bribes to secure contracts in India, Africa and the Middle East, including bribes to government officials, a practice banned by the Foreign Corrupt Practices Act. In response, Koch fired several employees and sales agents, including the business director of Koch-Glitsch France.

Disputed: Was Koch's response sufficient?

According to Bloomberg Markets Magazine's analysis of French court documents, Koch failed to hold higher-level officials accountable for the bribery payments. Koch said Koch-Glitsch's president for Europe and Asia "had no knowledge" of the misconduct. Koch also ended up firing the ethics manager who first conducted its investigation, and French labor courts upheld the firing as fair.

Context: Many corporations make bribes—and pay fines for breaking the law.

Many large companies have been investigated for bribery of foreign officials, including Hewlett-Packard and Motorola. The United States has recently stepped up its enforcement of the Foreign Corrupt Practices Act, including a preliminary investigation this year into whether News Corp. may have violated the act. A recent survey of business executives found that only 30 percent were "very confident" that their existing policies would prevent bribery.

Undisputed: Koch's European subsidiary sold petrochemical equipment to Iran, which seems to be perfectly legal.

While American companies have been banned from trading with Iran since 1995, Koch's European subsidiary, Koch-Glitsch, sold equipment to a unit of Iran's National Petrochemical Company for nearly a decade. The equipment helped construct an ethanol processing plant. Koch's legal counsel told the Washington Post that the sales totaled roughly 15 million euros over nine or 10 years, and that the equipment sold had "no military, weapons, or nuclear application whatsoever."

As Bloomberg Markets Magazine notes, while the sales to Iran may be controversial, they appeared to be legal since no U.S. citizens or U.S.-based divisions of the company were involved. Instead, Koch did the business at arms length through Koch-Glitsch offices in Germany and Italy.

Disputed: Was it wrong for a Koch subsidiary to do business with Iran?

Bloomberg Markets Magazine described internal documents demonstrating that Koch took a rigorous approach to following the letter of the law, but the article suggested more investigation might be appropriate. Koch's general counsel told the Washington Post that the company voluntarily ended all sales to Iran in 2005 or 2006. (Bloomberg Markets Magazine reported records of sales to Iran until 2007.) Koch dismissed comments by what it called a "disgruntled former employee" who told Bloomberg he felt the company's dealings with Iran had betrayed its stated core principle of integrity.

Context: Koch is one of many corporations that have done business with Iran.

Many other American companies, including Halliburton and GE, have done business with Iran through subsidiaries, and as the Washington Post's Jennifer Rubin pointed out, a few were still doing so after Koch ended its ties to Iran.

As well as these new criticisms of Koch's corporate behavior, the Bloomberg Markets Magazine article and Koch's response revisited several previously reported scandals, including millions of dollars in settlements the company paid after it failed to pay for $31 million worth of crude oil it took from Indian landmade false statements to cover up illegal emissions of the toxic chemical benzene at a Texas plant and accepted responsibility for the deaths of two Texas teenagers who died in an explosion caused by a leak in a gas pipeline with a well-documented history of corrosion.

Clarification: We originally referred to the Koch investigation as a Bloomberg story. It is from Bloomberg Markets Magazine.

Correction, Oct. 4, 2011: We originally referred to Koch-Glitsch as “France-based.” It has offices around the world, including in France; its main European office is in Italy.