Philosophy and science have a common underlying methodology with Russell. All knowledge is proved by the methods of science. As a mathematician he looks for reliable knowledge based on outer experience freed from all subjectivity. The stuff of mental and physical worlds is the same. There is no big comprehensive system. Atomism replaces any organic view in the sense that understanding one part explains other parts by inference. Otherwise his philosophy is a radical investigation of social and political questions. 
The work of Wittgenstein, this extraordinary thinker challenges accepted views in many disciplines. Impossible to summarize in a meaningful way. The interrelationship between language, thought and world establishes the basis of what can be known and not known. That philosophical statements are mostly meaningless and that philosophy is not a theory but an activity give a taste of his concerns. Meaning in language comes from its use, not, as is often supposed, from a source exterior to the word or sentence. His writings also propose new understanding of ethics, art and religion.