Simple climate models (SCMs) are numerical representations of the Earth's gas cycles and climate system. SCMs are easy to use and computationally inexpensive, making them an ideal tool in both scientific and decision-making contexts (e.g., complex climate model emulation, parameter estimation experiments, climate metric calculations, and probabilistic analyses). Despite their prolific use, the fundamental responses of SCMs are often not directly characterized. In this study, we use fundamental impulse tests of three chemical species (CO2, CH4, and black carbon – BC) to understand the fundamental gas cycle and climate system responses of several comprehensive (Hector v2.0, MAGICC 5.3, MAGICC 6.0) and idealized (FAIR v1.0, AR5-IR) SCMs. We find that while idealized SCMs are widely used, they fail to capture the magnitude and timescales of global mean climate responses under emissions perturbations, which can produce biased temperature results. Comprehensive SCMs, which have physically based nonlinear forcing and carbon cycle representations, show improved responses compared to idealized SCMs. Even the comprehensive SCMs, however, fail to capture the response timescales to BC emission perturbations seen recently in two general circulation models. Some comprehensive SCMs also generally respond faster than more complex models to a 4×CO2 concentration perturbation, although this was not evident for lower perturbation levels. These results suggest where improvements should be made to SCMs. Further, we demonstrate here a set of fundamental tests that we recommend as a standard evaluation suite for any SCM. Fundamental impulse tests allow users to understand differences in model responses and the impact of model selection on results.