Hellenic Polytheism and Neopaganism
Worship of the Greek gods is frequently incorporated into the practice of neopagan religions; it is not termed 'reconstructionist' as it does not intend to specifically revive ancient practice.
While there are some neopagan groups and practitioners that make associations with Greek deities, many forms of neopaganism do not require practitioners to dedicate themselves to a specific pantheon, ethical code, or worldview. Many Neopagans see the deities of diverse cultures as being different expressions of one goddess and one god, or even, ultimately, a single godhead (see Neopagan concepts of the divine and Wiccan views of divinity), this is different than the view of most Hellenic polytheists, especially reconstructionsts.
Magic is a source of much controversy within Hellenic circles. Some find the practice of any magic irreligious. Magic is not often used within a reconstructionist framework as there is little academic material to suggest that it was used widely in ancient religion.
Most Hellenic polytheist groups unequivocally state that reconstructionism is not the only correct method of reviving the Hellenic religion, but do identify a practice as Hellenic only when it embraces the humanistic values and ethical virtues of the ancient Greeks, demonstrates loyalty and reverence toward the Greek gods, and uses a religious structure that would be recognizable to an ancient Greek. These groups make a clear distinction between themselves and the Neopagan movement, and identify some 'Hellenic' groups as "simply disguised as 'Hellenists' for reasons that exist hidden within the depths of their own minds."
Read more about this topic: Hellenic Polytheistic Reconstructionism