During World War I British tanks were involved in 3060 separate battles, French Tanks were involved in 4356 battle and American tanks in 250. Germany was slow to adapt to the idea of tanks so that their tank presence during WWI battles was practically non-existent.
Still, despite their success in WWI, the future of the tank looked quite bleak during the years following the war as most of the countries involved were almost flat broke - especially the British and the French. One sure way to bankrupt your country is to enter into a full-scale war with other countries. By the end of the Great War Britain had 25 tank battalions, yet after one year, with the dangers of war slipping from people's memories and economies on a down turn, there were only 5 British tank battalions.
The future of the tank was never really assured in Britain until 1922, when the government decided they definitely needed to maintain a tank corps. On the other side of the Atlantic the Americans had decided to abolish their tank regiments altogether and handed over the few tanks they maintained to the infantry. This was partially due, no doubt, to the fact the Amercian government had decided on a policy of non-involvement in future conflicts. France did retain some remnants of a tank corps, but only as support for their 'mighty' army and a re-emerged cavalry, which had already been proved to be obsolete.
The only tank action during this quiet period after WWI was undertaken by the tank element of the British Army Occupation in Germany, aside from a small group of tanks that were sent to Russia to help the struggle against the Bolsheviks. In fact the usefulness of the tank could not be better displayed than during this time where a single British tank captured the entire city of Tsaritsin. Perhaps even more interesting to tank and war enthusiasts though is the fact the Tsaritsin was later renamed Stalingrad, the city the entire German army failed to capture in WWII.
Despite there having been a bit of a slowdown in tank production, the 1920s was a wonderful time of feverish activity amongst theorists pondering the possibilities of armored fighting vehicles. This was especially the case for the duo Fuller and Liddell Hart who published a whole series of books in Britain on the theory and practice of armored warfare. Most of these books were overlooked in Britain and America, but the Germans were avid readers of these publications. In fact many of the 'innovative' weapons used by the Germans for the first time in World War II were actually ideas that had been created by British and American theorists and inventors during this period, that were ignored by their respective governments at the time and left to carefully rot away in patent offices where the Germans were happy to read them. A fine example of this is the V2 Rocket - when quizzed by allies after WWII on where they got the idea from for their deadly rockets, a scientist simply replied 'ask Goddard', meaning Robert Goddard, the American inventor of the liquid-fueled rocket and space travel theorist. The Germans were also the first to make jet aircraft, jet fighters, in WWII, perfecting work started by Frank Whittle of Britain in the period between the wars. So the Germans had decided to learn all they could from their previous enemies in WWI, emulating their techniques then perfecting them. The Japanese did the same thing after WWII when, after being shocked that the Americans had the technology to split the atom, they decided to learn from their victorious enemy's scientific knowhow and lead the world with technology instead of might.
So, while the rest of the world was deriding the use of tanks Germany, despite signing the Treaty of Versailles and swearing not to amass an army, was learning from their defeats, reading modern theories written by their old enemies and secretly building the most advanced mechanized army the world had ever seen.
The prejudice against tanks was eventually overcome in Britain by 1926, but full-scale mechanization of the army was a plodding, slow affair that still was not complete thirteen years later when she declared war with Germany in 1939. The slow progress was not due to a lack of designers and available factories in America and Britain to make cheap tanks however, more a general dragging of heals by governments and people who'd frankly had enough of war and spending money on it.
The Russians entered the tank scene in 1929, with a five year plan to build as many tanks as possible. A plan which they followed through with, but it was poorly executed and produced very low quality tanks for the time. Stalin had not helped matters when he undertook his Great Purge, a tyrannical campaign of repression that effected almost every quarter of Russia and, ironically, ridded Russia of the theorists advocating the works of Fuller and Liddell Hart, whose works the Germans had read while developing their tanks.
Hitler was a huge advocate of the tank, so when he came to power in 1934 he dropped any pretence of adhering to the Treaty of Versailles and ordered his factories and designers to up production and began building tanks and other AFVs on a massive scale. Hitler setup the Panzerwaffe's (Tank Arm) first three divisions in 1935. A curious coincidence occurred during this time in that a civil war broke out in Spain and General Franco invited Hitler to help him defeat the Spanish generals who fought against him. Hitler happily obliged and used to opportunity to train his soldiers, Panzerwaffe and Luftwaffe (Air Arm). It was during the Spanish Civil War that Hitler's Luftwaffe invented and perfected a style of fighting called Blitzkrieg (lightning war), the 'shock and awe' tactics of the time, in such places as Guernica, which was utterly devastated by German bombers killing hundreds of people and General Franco's army coming in two days later to overrun the town. The event is the subject of a painting by Pablo Picasso, simply named Guernica.
The Germans, in particular a man named General Heinz Guderian who invented much of the tactics and training involved in the Spanish Civil War, envisaged an army of mixed forces, not simply all tanks as Fuller theorized, incorporating soldiers, air-forces and various Armored Fighting Vehicles, with the new panzer being the primary force striking at the enemy in the upcoming war they were preparing for.