There is controversy about climate change...  Yet, the serious scientists in both camps have clearly established that the surface of the earth has been warming up...

This warming is estimated at a certain amount (0.1 degrees C average) per decade (now around 0.2 degree C) for the last 150 years... Gus' present estimate is for a full one (1) degree C increase for the next 10 year. I could be wrong, but considering the sun is awakening and El Nino is about to come back, I may be right.

Most of the controversy is centred on the origin of this warming.

Up until the industrial revolution, humans used mostly surface available carbon such as wood from trees and a little oil from tar pits and a little coal from shallow mines.
Humans had had only a limited natural impact on the planet till then. 
Then came "fossil fuels". The usage of fossil fuels releases carbon dioxide into the atmosphere, adding to the natural carbon equation with carbon that had been sequestered as far back as the Carboniferous (350 -300 million years ago approx). Though much of this carbon is still sequestering naturally today, 3 to 6 ppm of CO2 per annum is not sequestered and remains in the atmosphere. 
Since the industrial revolution, humans have added about 125 ppm of CO2 in the atmosphere. (Gus' figure)
knowing versus using...
One of the tremendous ability of our species is to ask questions and analyse on who we are and where we are.
For the last 120 years, science has made some extraordinary strides and daily there are new discoveries or new ideas, most refining our knowledge away from fantasies — as proposed by religions. Science is not a religion.
And science has made mistakes, has often recognised its errors and in some areas scientists have had some vigourous debate trying to reconcile observation and theory. Global warming is not one of those blunders... Global warming science, despite some "uncertainties about the next effects", is 99.9 per cent accurate on the origins. Most (more than 95 per cent) scientists know that human burning of fossil fuels is inducing global warming. But the minority of the scientists disputing this theory get the bigger slice of the media's attention.
The major problem here is that human's present endeavours rely nearly exclusively on burning fossil fuels... There is a lot of cash to be made in selling fossil fuel energy and there is no monetary value in reducing our usage of fossil fuels. Greed trumps knowledge...
We live on a relatively small planet upon which our growing population is having a growing enormous impact on the surface environment from cultivation to industries, husbandry to polluting.
Albedo
One of the observation/theory conundrum relates to albedo or the reflectance of sun heat from planets back into the cosmos. This of course has a bearing on the earth's "global warming", which is presently observed... A light coloured surface will reflect more than a dark coloured surface, thus a light coloured surface is likely to make a planet "cooler"... 
These characteristics have been calculated with remarkable precision and a lot of scientific work has been done to tell us that presently (this now is important) due to the albedo the average temperature of the earth is around 15 degrees C. Should the earth be covered in ice (high reflectance) the temperature would drop below minus 40 degrees C. Should the earth be covered by oceans (lower reflectance/ more absorption of heat), the surface temperature of this planet would be around 27 degrees C. All this albedo calculated without change in the gaseous mix of the atmosphere.
One of the main variable when studying global warming and albedo is the presence of clouds (opaque water vapour). Some clouds will have a high albedo (high degree of reflectance) while some clouds will have a low albedo (despite being white, they let heat and light through, and trap infrared radiation below). Thus albedo of clouds can range from low (0.1) equivalent to asphalt to high (0.9) equivalent to snow...
Thus any global warming calculation need to take into account the albedo average for the surface of the earth — at various times — due to cloud cover, or not — and the melting of the ice that decreases the albedo, yet absorbs energy away from the atmosphere to melt in a complex feed-back-plus mechanism (I call a feed-back-plus mechanism a mechanism in which extra input is added into the feed-back loop.
About 4 billion years ago was what has been called the "faint sun paradox"... It has been calculated by some serious scientists that the earth then would have been mostly covered with water. The albedo would have been sufficiently low to counteract a much cooler sun. Since that time, the sun's intensity has grown 25 to 30 per cent. This is in line with observation/calculation of "evolving" stars. 
Thus the scientists estimated with a high degree of precision/calculations that despite the cooler sun, the earth did not freeze over, but enjoyed similar temperatures as today. The albedo of the ocean reflectance was enough to maintain this temperature. Greenhouse gases would have been needed in super-high concentrations in order to achieve a similar result — concentrations that do not appear in the geological record — hence the so-called "paradox".
The atmosphere albedo (reflectance of the sun heat) is about 0.3 (30 per cent) on average.
The seasonal variation do also affect the albedo greatly, especially in regard to oceans covering more of the southern hemisphere than the northern hemisphere...
There has also been specific studies of the geological record that show on average, CO2 amount in the atmosphere and the earth surface temperatures are "dancing" together, once other factors such as proportion of oxygen (a cooling gas) in the gaseous mix is taken into account. For example Arrhenius calculated that the last ice age saw about 45 per cent less CO2 that there was in 1890. Presently we have MORE THAN 200 per cent on the amount of CO2 in 1890. 
It has been demonstrated that CO2 is a gas that absorbs infrared radiation (thus greenhouse warming). It has been postulated that CO2 also affects the behaviour of water in the atmosphere. Gus says: Imagine adding a drop of dishwashing liquid in a bucket of water... Suddenly, the "surface" water tension is modified RIGHT THROUGHOUT THE BUCKET...  CO2 might be possibly changing the dew point at which water vapour becomes cloudy or not. A slight variation of the dew point will change the level at which cloudiness occurs. In contrast, more heat also means more evaporation (from the sea) which means higher humidity which in turns can change the dew point to create low but "warmer" clouds.  (Some scientists describe CO2 as a "trigger" mechanism)...
A storm will have a high reflectance, thus lower temperatures below it but higher temperatures around it plus the Coriolis force can turn such differential into a fierce hurricane, cyclone or typhoon. Other storms are generated from the interface of warm and cool air masses. The most severe of such interface results in tornadoes.
As the surface of the globe is warming up, what can we make of all this? In most of the record from about 1 million years ago, we can see that a difference of CO2 from 100 ppm to 300 ppm is "always" associated with a difference of temperature of up to 8 degrees C (10.5 according to some serious journals)...
100 ppm to 300 ppm of CO2 is in the realm of "natural" atmospheric carbon equation. Fires, trees, seas in cycles of photosynthesis, absorption and release. Yet the temperatures are linked to this cycle via the behaviour of the atmosphere in the lowest 10,000 metres, where water vapour (a greenhouse gas) can be either cloudy or clear... changing the albedo, in a loop until a new cycle begins... 
Presently due to human activities, the atmospheric CO2 level is around 410 ppm. You work it out. 
(Updated 2 july 2019).