"Mayans" is a very wide-ranging term because it happens to refer to something like thirty different cultures who speak Mayan languages, which are all related to the same extent the Indo-European languages are. People often use the term to refer to the Classic Maya, who occupied numerous city states in the Yucatan Penninsula during the Classic period (~250-900 AD), before their "collapse." There was no collapse, however, and Mayan cultures continued to thrive after this, into the Postclassic (~900-1520), and millions of Maya still speak Mayan languages today. With that out of the way, Mayan groups have long communicated in various ways with the people of Central Mexico, of whom the Mexica (Aztecs) were the last ruling group before the Conquest, and end of the Postclassic.

Since Mayan texts began to be thoroughly deciphered a few decades ago, we have learned that there was some sort of invasion, or at least heavy influence on the Classic Maya from the Central Mexican civilization known as Teotihuacan, starting in the 370's AD. We know of a warlord named Fire Is Born (Siyaj K'ak') who came to the Maya Area on the behalf of a person named Spearthrower Owl and possibly killed the king of Tikal, replacing him with Spearthrower Owl's son, who began a new dynasty. The son, Yax Nuun Ahiin I, is portrayed in extremely Teotihuacano-style clothing, and the art and architecture of the region begins to show heavy influence from Teotihuacan from now on. In the past, the theory held that Spearthrower Owl was the king of Teotihuacan, and he had invaded the Maya Area and installed new dynasties with his kin. Nowadays things are less clear. It's not understood who Spearthrower Owl was, exactly, and it's thought possible that Teotihuacan never even had kings. Yax Nuun Ahiin I's grave has also been found, and isotopic evidence seems to show that he grew up in Tikal, and never even set food in Central Mexico. The mystery deepens as to how far the ties go, but that there were strong connections between the Maya Area and Teotihuacan is undeniable from the artistic and architectural influence. There's also the fact that there was a "Maya Quarter" in Teotihuacan, where Mayan people lived, produced their own art, and held their own religious rituals, so there were clearly cultural ties going both ways.

Stepping aside from Tikal and other Mayan sites with heavy Teotihuacan influence, there are actually sites in Central Mexico which possess Mayan influence. One of the most famous is Cacaxtla, a site near Tlaxcala and Puebla with extremely Mayan paintings. The origin of this site isn't perfectly clear, but from later historical texts written after the conquest we have the suggestion that Mayan people from the Gulf Coast migrated and conquered (or intermingled) with the people of this area around the mid-Classic (~400-500 AD). It seems to have become quite powerful at the end of the Classic, but it faded by the transition to the Postclassic.

Also in Central Mexico (this time to the West of Mexico City) we have Xochicalco, a city which possesses interesting Maya-style friezes combined seemingly at random with much more expected Central Mexican-style feathered serpents. The friezes in question I'm describing are on the Temple of the Feathered Serpent. Xochicalco may be connected to Cacaxtla in that they both may have been founded by the same Mayan group that spread from the Gulf Coast in the Mid-Classic. It seems to have survived until the end of the Classic as well.

The transition from the Classic to the Postclassic in Central Mexico seems to have had a lot to do with the arrival of the Nahuas, a migratory group that soon became the dominant culture of Central Mexico, yet spread quite far, even down into Nicaragua. Their migrations were likely as much a result and a cause of the civilizational "collapses" we see throughout the Classic to Postclassic boundary. The Mexica (Aztecs) were Nahuatl speakers and belonged to this cultural group, but they were one of the last to arrive in Central Mexico (as stated by their own records). According to later historical records from after the Conquest, the early Nahua set up a city state in a place called Tula, or Tollan, which we associate with a site called Tula to this day. We associate these later legends with Tula because it seems to have been the center of a hegemonic empire that controlled much of Central Mexico until the mid Postclassic, when more southerly states around Lake Texcoco (such as the Mexica) took over. Anyway, the relevance to our relations with the people of the Maya Area link to the Toltecs (the people of Tula) insofar as there seem to be a lot of artistic connections between Tula itself and the famous Mayan city of Chichen Itza.

Chichen Itza was a site that survived the Classic to Postclassic boundary, but changed quite significantly. Early on it was more or less a normal Classic Maya site, with great Puuc and Chenes style architecture which can be seen in the older sections of the city to this day. Later however, after the Postclassic began, we begin to see art and architecture that seems heavily reminiscent of the art of Central Mexico. The famous ball court, the Tzompantli (skull rack), El Castillo (the pyramid), and the "House of the Warriors" are all particular examples of much grander, more monumental architecture that seems heavily influenced by the far away region. In some cases, such as the House of the Warriors, we see direct influence from Tula itself. Now, this influence is heavily debated. Like the influence of Teotihuacan on Tikal and other Classic Maya sites, it was once thought that Chichen Itza was directly conquered by Tula, and was something of an outpost of its culture. Now it's thought that the artistic style shift is an example of strong cultural transmission. But we could eventually gather more evidence that shifts the perspective another way, and it's possible there was a mix of things going on. It's clear anyway, that there was a tremendous Nahua influence on the Maya area during this time.

During the late Postclassic, when the Aztecs themselves finally take the scene, we see Nahuatl become a sort of lingua franca amongst Maya traders of Campeche and other groups up the Gulf. The Aztecs were also slowly conquering more and more down into the Ithsmus of Tehuantepec, and Moctezuma's immediate predecessor (Ahuizotl) had even conquered as far south as parts of Southwest Guatemala. There was much direct contact between the Aztecs and the Maya Area in this time, with people and traders moving goods and ideas back and forth. It's not for nothing that Mesoamerica, despite its extreme diversity of languages and cultures, shares an incredible amount of cultural features.

There are answers by /u/throwaway_the_fox and /u/400-rabbits and /u/Pachacamac, among others linked in the recent thread Did the Incas and Aztecs know about each other? which will be of interest to you. Someone else might gave more to contribute.