They did and the most famous writing system of them all are Maya hieroglyphics which researchers have only just been able to translate in the past few decades. In pre-Columbian Mesoamerica there are two types of writing systems. One type makes use of a system of pictographic symbols that act as a mnemonic device to recall already memorized things like myths. The Aztecs made use of a pictographic system as well the Mixtecs and the earlier Teotihuacanos.

The other type of writing system was one made up of glyphs. These glyphs consisted of different parts or elements which acted as indicators for a phonetic sound. Sometimes, though, glyphs turn out to be a logogram and logograms are glyphs which have a specific meaning known only to the writer or reader. Sometimes logograms can be translated because they are spelled out phonetically elsewhere in a text, sometimes they remain as single glyphs and are untranslatable since epigraphers lack that insider knowledge. The most famous writing system that used glyphs, as I mentioned, is the Maya writing system. To pull an example from them, in order to spell the word "bean" you would make use of the b'u and la phonetic elements to create the glyph b'ul. But the Maya writing system is not the only one to make use of a glyph system like this. The Zapotecs of Oaxaca had their own writing system, as well as the Epi-Olmec of Veracruz which are the Late Formative to Classic period descendents of the more well known Early and Middle Formative Olmec. Other glyph using systems include Isthmian script used in the area of the Isthmus of Tehuantepec as well as Ñuiñe from the Mixteca Baja, but Ñuiñe seems to straddle this grey area between a pictographic and glyphic systems of writing.

But to answer your contact question, it might be better for you to check out our FAQ section Pre-Columbian Trade and Contact which covers that topic quite nicely.