These Robotic Synthetic Creatures intent is to drain planet resources, Disable Reproduction, and turn the entire planet's species into Synthetic Soldiers. How they got rid of Children is unknown, but how they disabled Reproduction, they used a reproductive suppression field to stop all vital proteins that are required for children. The Synths vary in shapes, sizes, and in species, but after the combine took control of the earth, they began recruiting humans for the Combine Overwatch. How they make the humans into soldiers is unknown, but the anatomy of the Combine Transhuman Soldiers is shown in graffiti scattered across City 17.
How the combine took over the earth is shown on the Half-Life Wikia, but the war that took place was called "The Seven Hours War."
The Fall of the Combine Overwatch.
After the destruction of Nova Prospekt, The citizens of City 17 Rose up and fought for freedom, under the command of Gordon Freeman, and soon after, the destruction of the Citadel caused a massive super portal to form, so the combine would be able to call reinforcements from their home planet. As stated by Eli Vance in Half Life 2 Episode 2, "If the super-portal matures it'll be the Seven Hour War all over again... except this time we won't last seven minutes!"At the end of Half Life 2 Episode 2, the super portal is destroyed via a rocket from an abandoned Missile silo, but the combine Advisors kill Eli Vance, and the story will continue in Half Life 3/Half Life 2 Episode 3.