Although pre-Kantian modern philosophy is easily (perhaps too easily) organized as a debate between Rationalists and Empiricists, modern philosophy after Kant presents a much greater tangle of influences. The Flow Chart of Modern Philosophy after Kant below attempts to produce some kind of organization and representation of schools and influences. Note that the Continental tradition spreads out into a least four major trends, which then begin to overlap with each other and, ultimately, with Anglo-American schools. The Anglo-American tradition, succeeding British Empiricism, exhibits relatively contentless and sterile doctrines, like "Pragmatism," then begins to adopt similar doctrines from the Continent, consistent with a native Scientism, like Logicism, Logical Positivism, and Linguistic Analysis, and then finally succumbs to a withering blast of Continental Nihilism from Existentialism and Deconstruction. A small Analytic remnant (people like Searle) is thus faced with a tide of skepticism, irrationalism, and obscurantism in a combined Anglo-American-Continental school of "Post-Modernism" -- no attempt is made to comprehensively list representatives of this popular but miserable movement.
The basic inspiration of this chart is the chart in Will Durant's The Story of Philosophy [Simon and Schuster, 1933, pp. 80-81]. Durant's version spans the whole history of Western philosophy from the Pre-Socratics to his own day. For much of the history of Western Philosophy it is a gravely deficient representation -- see the discussion that introduces Hellenistic philosophy. Durant includes only one philosopher between Marcus Aurelius and Bruno: In the entire Middle Ages, only Thomas Aquinas warrants mention, yet even he is conceded no thought independent of Aristotle. The only other Mediaeval person singled out is Roger Bacon, who thus stands as little more than a red flag for Durant's Scientism. Late Antiquity, which is the key to Mediaeval thought, is completely ignored. For his own day, Durant includes figures who are now wholly obscure (Renan, Eucken) and others who seem very secondary (Bergson, Croce, Santayana). In the chart here, not much effort is made to include contemporary philosophy professors who may be currently fashionable or considered significant. The selection is somewhat brief, random, and idiosyncratic. Rawls, Kripke, and Rorty are probably considered significant by most, but Kelley and Peikoff are only included as the heirs of Ayn Rand and certainly would not be considered important by most academics. In fact, they probably will not prove to be important philosophers. They do, however, represent a dissident tradition, outside of academic philosophy, that is in many ways more sensible and promising than the thought found in the universities.
The most valuable aspect of the Anglo-American tradition in this period, the Liberalism of Mill and Spencer, has also been largely swept under, in fashionable academic thought, by totalitarian Continental tendencies. Those tendencies began prior to Marx, with the socialist and authoritarian theories of Saint-Simon and Comte (not to mention the totalitarianism of Hegel and his apologia for the Prussian state) -- French Liberalism was found in economists and political thinkers, like Jean Baptiste Say and Frederic Bastiat, who are not represented here. Turning away from the classic American political thought of Jefferson, Madison, Thoreau, etc., the "Pragmatic" Dewey was a socialist and, at least for a time, a sympathizer of the Soviet Union; and many Logical Positivists were already fairly serious Marxists. From this follows the overwhelming leftist bias of academic philosophy, and academia in general, from the 1940's to the 2010's, despite the anachronism and incoherence of such a bias after the exposure of Stalinism, the fall of communism, and the persistent stagnation of Euro-socialist economies -- though politically, 1992-2012, voters are still turning to leftist solutions to leftist diseases in Britain, France, Germany, and the United States. These setbacks may be due to the circumstance that it has largely been conservative politicians and pundits who have supported the free market. The free market, however, and political Classical Liberalism in general, are not conservative forces and influences, but revolutionary ones. Conservatives are thus liable to find themselves ultimately uncomfortable, as various neo-conservatives have lately been discovering, with their implications. Freedom is corrosive of traditional mores and belief, to the horror of both conservatives and the trendy leftists resentful of the success of capitalism and, especially, the West.
Having been abandoned in its homelands, Britain and America, Liberalism ironically has revived through Continental influence, with a combination of Kantian Critical influences and Austrian economics. As Carnap had brought his Marxism from Austria to America in the 30's, F.A. Hayek brought the Liberalism of Austrian economics to America by the 50's, though with a philosophical apparatus (from Popper) less popular than Logical Positivism had been. "Post-Modern" epistemology is thoroughly Marxist, that "knowledge" is simply determined by "power relationships." The damage from this sorry recipe for tyranny is yet to be fully realized.
History of Philosophy