In this paper I give a brief overview on the distinction between arguments and adjuncts in English. After an introduction, definitions from the literature are represented. Then I analyze some argumenthood tests, which are frequently used in research. However, all of them have potential weaknesses and there are several in-between cases. Some such cases are investigated in the third part, where the issue of obligatory adjuncts and non-core participant PPs is discussed. Finally, I conclude that there is still a need for further research to get the ultimate answer for this dichotomy.