Input-output (IO) modeling has become the standard methodology for stress testing economic value chains against production and cost inflation shocks. Notwithstanding their widespread deployment, some deficiencies exist in the literature regarding investigations into the varied properties and extensive applications of these modeling frameworks, especially when applied for stress testing exercises. This paper addresses these deficiencies by focusing on how model outcomes are affected by the assumed origin of a shock-whether it is applied to final demand, gross value added, intermediate consumption, or total output variables. Moreover, we look on how different parts of the modeling framework interact, in particular between price and production equations. We also show the relation between the introduction of binary passthrough mechanisms and the asbence of geosectoral feedbacks, and more generally how the passthrough rates can be integrated in all Leontief stressing assumptions. We present a thorough review that integrates theoretical principles with practical applications, drawing on examples from the environmental stress tests (carbon price or biodiversity intactness) currently required of financial institutions, to illuminate the theories of IO modeling for stress testing.