As a starting point, here's basic data on corporate profits divided by GDP for the period since World War II. The red line on top is profits before tax; the blue line at the bottom is profits after tax. The recent rise in profits is clear. But it's also interesting to note that the 1980s and 1990s were a period of relatively low corporate profits, while profits were higher from the 1950s through the 1970s.
There are a bunch of different ways to adjust profits to get a more nuanced number, but the same basic pattern over time tends to show through of higher profits from the 1950s to the 1970s, lower profits in the 1980s and 1990s, and generally higher profits in the 2000s--with a downward blip in profits during the Great Recession. Here are a few thoughts about this pattern.
1) It's common for those pointing to high profits to assert that they are closely linked to higher levels of income inequality. From a long-run perspective, the connection isn't at all obvious. After all, inequality was much lower back in the 1950s, 1960s, and 1970s. The rise in inequality started in the 1970s, but corporate profits drop to lower levels in the 1980s and the 1990s.
2) As the figure shows, the gap between before-tax and after-tax profits was larger back in the 1950s, 1960s, and 1970s. Here's a figure showing that corporate taxes have become relatively smaller as a share of GDP over time. But much of the drop in corporate tax revenues as a share of the economy happened back from the 1950s through the 1970s, when corporate profits were fairly high. The recent rise in corporate profits since about 2000 is apparent both in pre-tax and in post-tax corporate profits. It's not a creation of the corporate tax system.
3) There's a tendency in public discourse to treat "profits" as essentially a synonym for "loot and plunder." For economists, profits are instead a signal conveying information. The problem lies in interpreting that information! Ideally, high profits are a signal that what is being produced by the firm is highly valued by consumers, and so it's a good time for firms to invest, expand output, hire more workers, and give raises to existing workers. Indeed, high profits provide the finance to help those steps along. High profits in the 1950s and 1960s, for example, were accompanied by (mostly) low unemployment and solid expansions of jobs and wages.
4) In contrast, the recent wave of high profits, especially since the Great Recession, don't seem to be combining with high investment, strong expansions in output and wages, and so on. There's some controversy on this point. For example, it may be that what we measure as "investment" in the US economy is conceptually outdated, because 21st century firms may not be increasing investment in machinery and equipment, but they are instead investing in intangible capabilities to provide new services in ways that conventional statistics don't capture. Unemployment rates have fallen more slowly than hoped, but they are now below 5%. Wages haven't risen as hoped, but there are some preliminary signs that they may be starting to do so.
5) In one way or another, profits do eventually flow back to the rest of the economy, but the mechanisms through which this happens have changed over time. For example, the high-profit companies of the 1950s and 1960s also tended to pay high rates of dividends to shareholders. Now, high-profit companies are more likely to use profits to engage in share buy-backs.
7) Like so many economic issues, the meaning of high corporate profits will be clarified over the next year or two with the arrival of additional data. If the next few years see growth in investment and wages, together with a sag in profits, and perhaps a wave of money flowing back to investors as part of share buy-backs and merger and acquisition deals, then these last few years will look like a transitional period after the Great Recession. But if profits continue to remain high, then other explanations become more likely. Some of the higher profits may be due to weakened compeitition between producers. A related theory is that many of the high-profit companies are technology companies where startups can be risky and have high costs, but when a company succeeds, it has built a community of appreciative users in such a way that the profits can be extraordinary and long-lasting.