Climate models are developed based on well-established physical principles applied to past and recent climate changes. There is considerable confidence that the models can also provide estimates of some climate variables (i.e., surface temperature, CO2 levels, ocean heat content). Despite advanced mathematical developments in the field of climate modeling, the existing climate models suffer from the following major limitations: first, the models do not consider that their estimations will be highly unreliable when a tipping point is triggered; secondly, many of the environmental tipping points are already triggered, however their existence is overlooked; and third, the existing climate models do not consider the interrelations among the tipping points (i.e., one tipping point can trigger other tipping points to be tipped more rapidly). Our objective is to describe the importance of environmental "tipping points," the importance of which is often ignored or downplayed in relevant literature. Our analysis, based on extensive multidisciplinary literature searches, reveals that there are many environmental tipping points which are overlooked in climate-modeling studies. We argue that climate modeling could be improved when the tipping points and their interrelations are all considered within the modeling process. We further discuss two other important issues regarding environmental tipping points: first, all tipping points might not be as impactful on the climate system, therefore their relative impacts should be ranked; second, it is in principle impossible to know the exact number of environmental tipping points, therefore even though it could be possible to devise improvements to the existing climate models with our suggestions, it may be impossible to achieve a perfect model to estimate the climate variables of the upcoming years. The remainder of this paper is structured as follows: In the background section, we introduce research on tipping points within commonly used climate models. We explain the aerosol masking effect and ocean dynamics with respect to their commonly overlooked roles as important contributors to environmental change. We introduce remote sensing and AI methods that serve as promising approaches for identification of currently unknown tipping points. We mention perturbation theory, a standard set of mathematical methods in physics that serves as a potentially systematic method to rank environmental tipping points according to their impact on extant climate models. In the discussion section, we make suggestions regarding further research on identifying the typically overlooked tipping points, and we make suggestions to improve climate models by considering additional information presented in the current paper. Finally, we conclude this article summarizing our chief methodological recommendations.