Interest rates are very low or negative because of a need for investors to find risk-free sovereign bonds. During the 19th century there were many years of crashes when the only safe store of value, besides gold, was Treasury bonds; at times the real yield was near zero. The nominal yield was also quite low.
Investors who buy bonds may engage in competition with other investors, thus forcing the price up, which makes the yield go down. It is like real estate investors: if too many buyers compete to buy a rental property to get yield from a property then prices will go higher and yields as a percent of the property will go lower.

   Since the great crash of 2008 (the GFC) governments have been mandating banks and insurance companies to have a higher percentage of investment grade bonds in their portfolios, thus creating an increase in demand for bonds. Since 2008 about half of the supply of investment grade bonds has been removed from the market either through paying down debt or by downgrades in credit quality.
Corporations have changed their attitude towards debt and are no longer reliable investment grade borrowers if rated BBB, thus to get a safe store of value then investors need to avoid BBB rated corporate debt. Investors seeking safety and predictability may find that BBB rated Muni bonds are unreliable and should not be held by those seeking genuine investment grade bonds. Mortgages and other types of non-governmental debt have the problem of frequent prepayment based on sudden refinancing manias. These frequent prepayments can disrupt a bond portfolio, making mortgages a less desirable store of value even if their default risk may be low. Thus, by a process of elimination, what is left standing as a reliable store of value are U.S. Treasuries which are non-callable. Thus investors have to pile on to this benchmark and this drives the price up (and yields down).

   The ratio of debt to GDP in the 1900’s was about 120% to 180%, except for wartime; it has doubled to 345% since 1998 when the great era of overpriced stocks began. Ironically this excess debt, because it has created a climate where debt default risk has increased, means that investors have a greater need to avoid the risk of a debt default, and thus they need to try harder to move away from non-governmental debt and instead move into Treasuries.
Many people say that yields are the lowest ever, however one should realize that during the 19th century the U.S. was going through a transformation where it was an economically underdeveloped country before the Civil war ended in 1865, and it continued to complete its path to become a Developed country by the early 1900’s. In 1913 the Federal Reserve was established, which was able to attempt to reduce risks of crashes and government debt defaults, etc. The crash of 1929 led to a New Deal legislation in 1933 that developed institutions like non-callable (by lenders) 30 year mortgages, FDIC bank insurance, etc.
The great crash of 2008 resulted in a new regime by financial authorities where they had to commit to aggressively bailing out giant institutions with new printed Federal Reserve issued money. This new era assumes that government debt increases are OK because they act to prop up the economy instead of viewing government debt as if it were a household’s debt where the household must avoid big debt. These improvements acted to make the U.S. economy less risky. A lower risk level implies lower interest rates, thus the drop in U.S. Treasury yields over 200 years is partly legitimate. Some of the decline in yields was an illegitimate manipulation by the Fed’s Quantitative Easing, which is estimated as lowering rates about 0.5% or 0.8%. But QE alone is not adequate to explain why rates are low.
The growth of globalization, mostly in the past 20 years, has resulted in a huge number of wealthy EM residents who don’t trust EM banks or EM currencies or EM governments and thus seek to invest in Developed countries. Even if the EM citizen only buys real estate, that in turn makes the American who sold his house, invest in Treasury bonds thus increasing the bond prices.
The Developed world’s AA or AAA rated sovereign debt is basically used as the world’s money. Using the 2 year U.S. Treasury as a benchmark, yielding 1.56% and assuming inflation on a forward basis will soon be 1.5% means that short term risk free real rate is about zero. The lower rates in the EU and Japan are because those countries are at much greater risk of falling into a debt recession while holding significantly more debt.
There is a significant probability that the world will go into recession and be overwhelmed by excess debt resulting in a wave of corporate and personal bankruptcies and investors will flee the tsunami to the high ground of Developed country Treasuries as a store of value. Bond spreads for corporate debt will widen (get higher) at the same time that Treasury yields will continue to drop.

    The Invisible Hand of the market is anticipating a deep recession caused by an unprecedented amount of debt and is thus now discounting the future with higher bond prices.
I prefer to look at solid fundamentals instead of looking at exotic derivatives to understand the situation. The key, powerful, undeniable fundamental is that there is a huge wave of disinflation caused by excess global capacity which is inherently deflationary. The Developed world is full of well paid workers who can’t compete with low paid workers who live in EM countries, thus Developed country economies are trapped in a deflationary debt default environment. Couple that with the excessive, unserviceable corporate and household debt and you have plenty of reason to believe in recession and low yields.

   Investors need independent financial advice about the risk of misunderstanding why yields are so low.