Logical Positivism and Analytic Philosophy emerged as influential movements in early 20th-century thought. They aimed to establish a scientific basis for philosophy by focusing on empirical evidence, logical analysis, and the verification of meaningful statements. Key figures like Bertrand Russell and Ludwig Wittgenstein shaped these movements. The Vienna Circle played a crucial role in developing and spreading logical positivism's ideas, emphasizing the importance of language, logic, and scientific methods in philosophical inquiry.