Sons of Ivan Kalita died young. Simeon the Proud died during the epidemics of plague and Ivan the Red died of an unknown cause, being only 31 years old. Simeon had no children and Ivan had two sons. This meant that the land of the Moscow knyazes was not split between the heirs, as it happened in other principalities. After the death of Ivan the Red, when no adult knyazes were alive, the yarlyk for the duchy of Moscow was given to the knyazes of Suzdal. But the ten years old knyaz of Moscow Dimitri Ivanovich began the struggle for his heritage. Metropolitan Alexy and Moscow boyars assisted him. He managed to convince the khan and soon received the yarlyk and the title of the grand knyaz of Vladimir. The knyaz of Suzdal Dimitri Konstantinovich was the grand knyaz for only two years.
In the first years, the state was run by metropolitan Alexy and the boyars. Later, when Dimitri grew up, he began ruling himself. He continued the politics of Alexy.
So, firstly, he insisted that the title of the grand knyaz and the town Vladimir are the private and inherited property of the Moscow knyazes.
Secondly, he interfered the affairs of Ryazan, Novgorod and other principalities and dictated his will. When Suzdal and Tver attempted to oppose him, he forced them to obedience. The conflict with Tver was especially long and stubborn. Knyaz of Tver Mikhail Alexandrovich asked Lithuanian knyazes for help and Olgerdas besieged Moscow, but couldn't take the city and returned to Lithuania. After that the Moscow army layed siege to Tver. At last, in 1375 the knyaz of Tver acknowledged himself "the younger brother" of the knyaz of Moscow and refused to compete for the title of the grand knyaz. Since then, Lithuania became an enemy of Muscovy. Dimitri also fought against Nizhny Novgorod and when they attempted to retain the independence, he forced them to pay 8,000 rubles of contribution.
Thirdly, Dimitri was the first who dared to oppose the Mongols after centuries of the occupation. This became possible because of the internal feuds in the Horde. Khans killed each other till the Horde fell apart into two hostile halves. During these feuds groups of Mongol exiles formed gangs which roamed and robbed Russian and Mordovian lands along rivers Oka and Sura. Since they did not represent the "official" Golden Horde, knyazes of Ryazan, Nizhny Novgorod and Moscow sent their armies against them and even local irregulars easily drove them away, chased and killed them. It was a good moment to test the growing strength of Rus. This made the khans to collect a large army against Rus. This army, led by Arabshakh, defeated Russians on river Pyana (a tributary of Sura) and sacked Ryazan and Nizhny Novgorod. Russians revenged by devastating the Mordovian lands, controlled by the Mongols (poor Mordovians... DM). Khan Mamay sent his troops to punish Rus. They burned Nizhny Novgorod and captured Ryazan. However, Dimitri of Moscow won the battle on river Vozha in 1378 and drove the enemy away from Muscovy.
So, by repelling the wandering robbers Russians got into an open conflict with the khans, who supported these gangs. These small victories provided good training and added courage to the Russians. Khan Mamay had to either give up control over Rus or re-conquer her. Two years after the battle of Vozha, in 1380, Mamay began a new campaign.
Expecting strong resistance, Mamay gathered a large army and contacted Lithuania, offering them a joint campaign. Jogaila, the successor of Olgerdas, promised to join the Mongolian army on September 1, 1380. Oleg, the knyaz of Ryazan, learned of the upcoming invasion, contacted Mamay and offered an alliance, trying to save his lands from devastation. Dimitri of Moscow had to collect all his allies, knyazes of Rostov, Yaroslavl and other cities. He also sent to Novgorod and some other cities to ask for help, but the help was late. However, his army was large enough to withstand the Mongols. Dimitri left Moscow in August 1380. Before he left, he visited Sergius in his monastery. The famous hegumen sent two of his monks to the Dimitri's army — Peresvet and Oslyabyá. First, the Moscow army moved to Kolomna on the border with the Ryazan principality, because they thought that Mamay will take the route via Ryazan. When they learned that the Mongols are moving further to the west to join their forces with the Lithuanians, they also went to the west, to Serpukhov. Russians decided not to wait for Mamay on the border, but to attack him before the enemies' armies merge. Dimitri crossed rivers Oka and Don and came to Kulikovo field, where river Nepryadva meets Don. Jogaila was one day's march away when Russians and Mongols met. Dimitri ordered a regiment led by Dimitri's cousin Vladimir Andreevich and a boyarin Bobrok to hide in a wood near Don. The army of Mamay attacked Russians and almost overcame them. Many Russians died and Dimitri himself was missed in action, he lay under a tree unconscious. And then the hidden regiment attacked. The Mongols didn't expect this strike and fled. The victory was decisive, but too may people were killed. Two years ago, in 1382, when a new khan, Tokhtamysh, who had dethroned Mamay, suddenly attacked Rus again, Dimitri did not have enough warriors and had to leave Moscow and go to the north. Tokhtamysh took Moscow, sacked it and burned. Other cities were captured, too. Dimitri had to pay tribute again and to send his son Vasily as a hostage to the Horde.
Nevertheless, the battle at Kulikovo field was an important mileston. First, it has shown that Russians can defeat Mongols. Second, in the eyes of the Russians, the knyaz of Moscow fought for all Rus, while Ryazan betrayed them and Novgorod failed to help. All minor principalities now eagerly accepted the leadership of Muscovy. So, the battle at Kulikovo field significantly accelerated the concentration of lands under the rule of the knyazes of Moscow.