I'll briefly touch on the Greeks but will focus on more modern bodybuilding which I am more familiar with.

The Greeks did have forms of resistance training to improve performance in sports and had training facilities ( I believe that is the root word of gymnasium). Arguably the most famous was Milo of Crete ( a wrestler) progressive overload of carrying a baby cow everyday. As it gained weight the task became now strenuous. This story is regarded as apocryphal since a cow gains weight at a pace faster than the body can adapt. As far as I know their was not formal body building competition where the physique was judged. They did have something akin to a dumbbell but it is believed to have been used in jumping events as a counterweight.

As to modern bodybuilding that has roots in strongman shows around the turn of the 20th century. Before that many strongmen were large and barrel chested eg louis cyr. This largely changed due to Eugene sandow.

Sandow started as a acrobat in his teens till he began to train under professor Attila who introduced him to weight lifting. Training at this time consisted of barbell, kettlebell, dumbbell, and body weight. Lifting of odd objects and static holds were also incorporated and were mainstays of performance. To my knowledge their were not squat racks and generally all lifts were performed from the floor.

At this point they toured the European circuit performing feats of strength. Eventually sandow branched out on his own. His shows included the usual feats of strength including challenges to the audience. One of his major innovations was his private showings. After a performance people could pay additional to view him close up including touching his muscles. Sandow would often perform and exhibit nude, wearing only a fig leaf, drawing inspiration from classical art, sandow also stated he desired to emulated classic proportions with his physique. This marketing of his status of a sex symbol at the end of the victorian highlights his savvy as a business man. (A similarity he shared with Houdini who also performed nude, or nearly) He expanded beyond shows to include books, weights, gyms, early bodybuilding contests, and marketing his training towards armed forces.

The major rivals to sandow were the Saxon brothers with the strongest being Arthur Saxon. At one show sandow hid in the audience and dramatically unveiled himself when saxon asked for challengers. The challenge was accepted and Arthur appeared to be able to lift overhead a weight sandow could not. This was overturned by judges who ruled sandow was incapable of fully extending his arm due to the development of his tricep. This then resulted in a odd court case, and accusations of a rigged barbell.

A brief note on differences from modern bodybuilding. The bench press had not been invented nor most exercise machines. This did not allow the training of the chest that would be seen later in the 20th century. Additional a well developed chest was seen as feminine due to resembling breasts. The tanning of modern bodybuilding was not seen, sandow was described as pale and to perform he would flex and have a pink powder applied to the protruding muscle groups to further accentuate the definition. Also it was widely called physical culture.

Physical culture and strongmen started to disappear with the shift from live entertainment in a music hall to silent film, WW1 occupying most men of the period, and the cultural obsession shifting from it with one author believing the popular increase of the bicycle became the new popular physical activity partly due to its coed ( popular with young ppl) and less overtly sexual nature ( popular with parents). It remained a significant part of many cultures but became absent from the world stage to the degree it was.

At this time the general idea of progressive overload was understood but not to the degree that would develop post Ww2 which would lead to modern programming stemming from seperate lineages including western weight lifters, Soviet weight lifters, and body builders, all developing developing different programs to achieve desired results.

Regarding specific movements the bench press was invented by George Hackenschmidt. Prior to that the floor press was used, with lifters laying on the ground and pulling the bar over their head and then pressing it. Jack lalanne invented the smith machine as well as different cable and selective plate loaded machines. Arthur Jones was a large innovator in machine design and programming in the 70s.

Bodybuilding as we know it ( instead of physical culture) started in the 30s but took off in the fifties. Mr America started in 1940, Mr universe in 1948, Mr Olympia in 1965 ( the now highest competition, started by the weiders). At this point more formalized competition and physiques as would be recognized now began with the emphasis being on the physique with no accompanying feats of strength. Modern competitive bodybuilding owes heavily to weider brothers who magazines and competitions defined the era and continue to influence the culture to this day.

This is mostly sourced from the encyclopedia of bodybuilding-schwarzenegger sandow the magnificent-chapman the perfect man- waller Houdini Tarzan and the perfect man- kasson Combat sports in the ancient world- poliakoff

For video info look into the rogue legend series

If you have more questions I can elaborate where I can. I am most familiar with early strongman specifically sandow. In my opinion popular acceptance of bodybuilding is almost solely due to Arnold Schwarzenegger but I do not have any real sources for that so I'm not going to go into that but I'm sure someone else can comment on that.

u/govschwarzenegger could elaborate and correct anything I have wrong since I am referring one of his books and he lived it.