The positivistic Received View construed scientific theories syntactically as axiomatic calculi where theoretical terms were given a partial semantic interpretation via correspondence rules connecting them to observation statements. This paper assesses what, with hindsight, seem the most important defects in the Received View; surveys the main proposed successor analyses to the Received View--various Semantic Conception versions and the Structuralist Analysis; evaluates how well they avoid those defects; examines what new problems they face and where the most promising require further development (...) or leave unanswered questions; explores implications of recent work on models for understanding theories; and rebuts the few criticisms of the Semantic Conception that have surfaced. (shrink)