Modern (theoretical) physics seems to be in deep crisis today as many of its core aspects are not empirically well-confirmed. Heated exchanges among physicists on the scientific status of physical theories with little or, at best, a tenuous connection to possible experimental tests is highly visible in the popular scientific literature. Some physicists (e.g., Carroll 2014, 2019; Ijjas et al., 2017) argue that science must discard empirical testability as one of its defining properties and the highly explanatory theories of present-day physics should be exempted from experimental testing, while others (e.g., Ellis & Silk 2014) spot in these arguments (for softening the testability or falsifiability requirement for modern physics) a dangerous tendency to undermine science. The philosopher of science who naturally draws most attention in these current debates is Karl Popper (1902-1994). His views, however, are often misrepresented in these debates. The prime objective of this paper is to explain how a more enlightened perspective on the ongoing debates can be obtained by a careful scrutiny of the Popperian criterion of falsifiability. As a first step in achieving this objective we will analyze the two major (conceptual) failures on which the current controversies rest. Our next step will be examining the controversial string theory to see whether the criteria of falsifiability is a ‘blunt instrument’ for determining its scientific status.