The idea of the subtle vital force (prana) and the channels along which it flows (nadis) appear in the earliest Upanishads (7th-8th century b.c.e.).  The heart was said to be the centre of the 72,000 nadis or subtle channels, and the place into which the senses are withdrawn during sleep.  As with many ancient civilisations (e.g. Egypt, Homeric Greece), the heart was also considered the seat of waking consciousness.

But it was only in the later Upanishads - the earlier of which were composed somewhere between the 2nd century b.c.e. and the 2nd century c.e. - reference is first made to basic Tantric concepts such as chakras, mantras, and so on.

The Brahma-Upanishad mentions the four "places" occupied by the purusha (soul): the navel, heart, throat, and head.  Following common tradition, each place is characterised by a particular state of consciousness: the navel (or the eye) waking consciousness, the heart dreamless sleep, the throat dreaming, and the head the "fourth" or transcendent state.  These four states, originally referred to in the Mandukya Upanishad, are identified with the gods Brahma, Vishnu, Rudra (a derivative of Shiva) and Akshara (the indestructable). [Mircea Eliade, Yoga, Immortality, and Freedom, p.128]

The Yogatattva Upanishad speaks of the "five parts" of the body corresponding to the five great or cosmic elements - earth, water, fire, air, and space.  Each element corresponds to a particular mantra - a "seed-vibration" or mystical syllable - and a particular deity.  Emphasise is also given to siddhis (supernormal powers) that can be attained through mastery of yoga and of the different elements. [Eliade, Ibid, pp.130-1]