CDOs attempt to manufacture safe assets from riskier ones. Various debts are pooled, then the pool is divided into 'tranches'. Each tranche has a different rating, indicating riskiness of the tranche, according to the tranche's claim on distributions. A higher rated tranche will get paid before riskier tranches, allowing investors to choose their risk tolerance. Riskier tranches have higher yields commensurate with a greater risk of not being paid.
In theory, this structure is sound, provided that the debt being pooled has known characteristics. During the financial crisis, ratings fraud contributed to the breakdown of CDOs [2]. Lenders made unsound loans and lied about the characteristics of the collateral and the borrowers. Ratings agencies (Fitch, Moody’s and S&P) then rated this debt as being less risky than it actually was, due to having false information and perverse compensation incentives. Additionally, structurers assumed that diversifying geographically would prevent correlated defaults on individual debts (which was not the case). These assumptions led to CDOs having unsound risk pools. More exotic products, like CDO squared (CDOs composed of CDOs), further amplified problems.
Similar products (e.g. CLOs) have been in high demand, as there is a genuine need for safe assets. Ideally CDOs can be produced without succumbing to the issues they faced during the financial crisis. The current interest rate environment exhibits suspicious behaviors, including negative yielding sovereign debt and investment grade/high yield spreads [3][4] roughly as tight as they were prior the financial crisis. Increasing the supply of safe assets may help lead to a rates environment that would previously have been considered normal.
[0] https://voxeu.org/article/safe-asset-shortage-rise-mark-ups-...
[1] https://en.wikipedia.org/wiki/Malinvestment
[2] https://macromarketmusings.blogspot.com/2010/01/academic-vs-...