Are American poverty rates increasing? What about global poverty rates
US

A snapshot of Poverty for the US is here. The key is Figure 5, which shows alternative measures of poverty, using different data and methods. (see text for details). Basically, they show that there is plenty of variation from alternative criteria, ranging from 0% to 5%. This is likely to be an explanation of why sometimes evidence seem to be contradictory. 

For the evolution of poverty, see this study. Unfortunately, it stops at 2010, but it is very comprehensive. Figures start in page 53. Basically, poverty has fallen recently, specially when measured in terms of consumption. This could be an indication that before the Great Recession, poorer individuals were living on loans/debt. There is plenty of evidence that consumption inequality is lower than income inequality, because individuals have a desire to "keep up with the Joneses" (the so-called Veblen Effect).

World

Here is the evolution of World Poverty since 1820:



Here is in relative terms (as % of world population):



Here is the current (2014) snapshot of poverty around the world:



An amazing analysis of World Poverty, in simple slides, is here.

A careful analysis of existing evidence is found here.