Simple climate models (SCMs) are central tools used to incorporate climate responses into human-Earth system modeling. SCMs are computationally inexpensive, making them an ideal tool for a variety of analyses, including consideration of uncertainty. Despite their wide use, many SCMs lack rigorous testing of their fundamental responses to perturbations. Here, following recommendations of a recent National Academy of Sciences report, we compare several SCMs (Hector-deoclim, MAGICC 5.3, MAGICC 6.0, and the IPCC AR5 impulse response function) to diagnose model behavior and understand the fundamental system responses within each model. We conduct stylized perturbations (emissions and forcing/concentration) of three different chemical species: CO2, CH4, and BC. We find that all 4 models respond similarly in terms of overall shape, however, there are important differences in the timing and magnitude of the responses. For example, the response to a BC pulse differs over the first 20 years after the pulse among the models, a finding that is due to differences in model structure. Such perturbation experiments are difficult to conduct in complex models due to internal model noise, making a direct comparison with simple models challenging. We can, however, compare the simplified model response from a 4xCO2 step experiment to the same stylized experiment carried out by CMIP5 models, thereby testing the ability of SCMs to emulate complex model results. This work allows an assessment of how well current understanding of Earth system responses are incorporated into multi-model frameworks by way of simple climate models.