Humans don't possess any natural magical abilities, and are physically inferior to demons. Most humans are no match for even the weakest of demons, although some who have trained for years and who possess appropriate weapons and equipment, such as Devil Hunters or the Order of the Sword, are able to combat and defeat demons. Some humans are shown to be able to cast magic, but it seems that this ability comes from using demonic power.
Other humans attempt to overcome their inherent weakness by obtaining demonic power through complex rituals: Arius (who summoned Argosax with the Arcana in Devil May Cry 2), Arkham (who became a demon by killing his wife in Devil May Cry 3), and most of the Order of the Sword (who performed the Ascension Ceremony to become artificial demon-human hybrids in Devil May Cry 4) took this approach.
Despite these drastic differences, and the general enmity between the two species, humans and demons can fall in love and mate, producing natural human-demon hybrids. Sparda and Eva are the most prominent example of this, though Bradley and Angelina Hagel go through a similar romance in Devil May Cry: The Animated Series.