Automate modifications between local test and remote server

there was a post 3 years ago on this topic which was closed. Here. I wonder if that forum member has accomplished his task? Anyone?

I am currently setting up my local site with WAMP. I have a hosted remote site also. I cannot seem to find anything that automates the relationship between the two. Kind of like an update button that I press when I have made changes to the local host version of my website, which automatically updates the remote hosted site to go live with the modifications. I have weekly updates to perform, hence my need to simplify the process.

Any news on this idea being accomplished by anyone?