Global warming is arguably one of the most pressing sci-entific issues of the last decades since it impinges directly on societal, economic, and environmental aspects of the world we live in. The fundamentals of the science under-lying the forecasting of climate, and anthropogenic climate change, have been published and debated long before making headlines. In fact, the foundation of our understand-ing about the so-called “greenhouse effect” in relation to the earth's surface temperature is almost two centuries old. The greenhouse effect refers to the radiative process by which a planet's atmosphere warms the surface to a tempera-ture above what it would be without it. The sensitivity of the earth's climate system to changes in atmospheric carbon di-oxide (CO2) was estimated at the end of the nineteenth cen-tury with an earlier allusion to a greenhouse effect credited to the French physicist Fourier. The rise of the atmospheric CO2 concentration was discovered about fifty years ago and the compelling evidence of anthropogenic climate change to global warming stated in the IPCC (2014) report.The purpose of this short communication is to briefly over-view some of the fundamentals behind the natural and an-thropogenic greenhouse effect. Some values to quantify the magnitude of the natural and anthropogenic forcings using a simple but physically-based climate model are provided, and conclude with a short acknowledgement of the contri-butions of the first scientists whose pioneering and seminal works aspired to develop comprehensive numerical models to understand and forecast global warming and its conse-quences.