Final answer:
Humanistic Therapy, developed by Carl Rogers, emerged in the 1950s and has significantly influenced the field of psychology.
Step-by-step explanation:
The therapy that began emerging in the 1950s is Humanistic Therapy, and the individual credited with its development is Carl Rogers. He developed a client-centered therapy method that has been highly influential in clinical settings. Carl Rogers, along with Abraham Maslow, played a vital role in shaping humanistic psychology, which focuses on the potential of all people for good and the growth potential of healthy individuals.