Both Western  and Taoist alchemists supposedly had the power to change base metals into gold, could prolong their lives with occult formulae, and were capable of seemingly magical feats. But alchemical traditions also reflect a strong vein of mysticism, with so-called alchemical transformation taking on the appearance of spiritual advancement and personal growth.
Vague hints of a deeper mystical significance always simmered just under the surface for Western alchemists. Zosimus of Panopolis (3rd cent. CE), for instance, told an allegory about an alchemist who was sacrificed.  Scholars have interpreted this as reference to the degradation of base metals as they are transformed into gold. But it’s also been interpreted as the transformation of the alchemist himself, as he is transformed into metaphorical gold, obtaining union with the divine or enlightenment. The psychologist Carl Jung (died 1961) took this story as the jumping off point for his model of psychological development. According to Jung, a person has to face his dark side (aka, hit rock bottom or, in Zosimus’ words, be sacrificed) in order to achieve his full potential. Transformation/healing takes the form of a marriage between the conflicting aspects of a person’s personality.  Language like this is reminiscent of the early seventeenth century Chemical Wedding of Christian Rosencruetz, a strange story about the marriage of a king and a queen that’s been interpreted as an allegorical description of the alchemical process, as myriad ingredients are combined to produce gold. 
For the Taoist alchemists, success in their craft was in large part dependent on knowledge of the Tao, or what Western alchemists might have called the working of the world (seen and unseen). Taoists, like Western alchemists, believed that there was an order to the universe which could be understood via the sort of experimentation with which alchemists are traditionally associated. Alchemists in both East and West also held a unified theory of existence, wherein everything was connected. This unity, which the Arabic alchemists called wahdät-ul-wujûd, meant that nature was inherently mutable. As evidence of this, alchemists pointed to examples of transformation in nature, such as insects undergoing metamorphosis. According to Taoists like Zhang Wumeng (10th cent.), the “second life” of an insect was proof that “humans can transform into immortals.”  And the transformation of one kind of metal into another was thought to be but another demonstration of this recognized law.
A gifted ghost-hunter and Taoist by the name of Li Hao (11th cent.) explained how transformations of this sort could extend a person’s life: Existence is comprised of five elements. Humans possess a portion of these elements within themselves. “While alive, we recognize a distinction between things and self; inside is self, outside are things. As long as the sense of things and self is not forgotten in the mind, self and things are divided, so the energies of the five elemental forces one receives are disconnected from the five elemental forces at large.” Once humans used up their portion of the elements, they died. But “if you genuinely forget the difference between things and self, causing this body to commune with heaven and earth as one, then the energies of the five elemental forces will circulate inside and outside without exhaustion.” 
According to some Taoist alchemists, personal morality had a bearing on the degree to which a person could achieve this transformation. Zuo Ci (3rd cent. CE), for instance, discovered an alchemical scripture in a cave, but refused to pass his learning onto the rulers who sought out his wisdom, saying that their immorality made them unfit for alchemical research. Zuo Ci and his fellow Taoist alchemists took to the mountains, seeking the seclusion that’s integral to the self-analysis typical of mysticism and the psychological development advocated by Jung. 
Another Taoist alchemist, this one by the name of She Fashan (died in 720 CE), obtained mastery over ghosts, exposed false alchemists, and practiced both divination and medicine. The emperor called him to court and tried to heap him with honors, but Fashan endeavored to remain aloof, committed to his study of the Tao, in which “the unknown is silent and hard to fathom and the imperceptible is immeasurable.” 
The contemplation of paradoxes and mysteries was integral to the inner transformations associated with alchemy: The inversion of logic disintegrates the categories that prevent us from appreciating the unity of things. By understanding how everything is connected, alchemists believed that they could transform themselves and the world.
Today, the notion of “alchemy” is something of a joke—to think that people actually thought that they could change lead into gold or live forever—and many so-called alchemists were certainly frauds. But this is unfair to alchemy as a whole. Many alchemical textbooks reflect mystical traditions that eschew the sort of greedy immorality that alchemists are accused of cultivating. Experimentation along these lines laid the groundwork for modern chemistry (resulting, for instance, in the discovery of processes for producing silver nitrate, arsenic regulus, ammonium carbonate and lead acetate). And quantum physics is beginning to confirm the notion that everything is, in fact, connected. 
So maybe the alchemists weren’t so crazy after all.
1 By Western alchemists, I mean those active in the ancient Greco-Roman world regardless of their ethnicity (including alchemists who made use of/composed texts supposedly derived from Egyptian and Persian sources), Persians, Muslim-Arabs (who made great strides expanding upon the work of Persian and Greco-Roman alchemists), and Medieval Europeans (who benefited from the work of Muslim-Arabs). On Greco-Roman alchemy see Georg Luck’s Arcana Mundi. On the alchemical strains in Greco-Egyptian alchemy see Garth Fowden’s The Egyptian Hermes. On Persian and Muslim-Arab alchemy see Kevin van Bladel’s The Arabic Hermes. On Medieval European alchemy see John Read’s From Alchemy to Chemistry.
2 A resident of Roman Egypt, Zosimus was probably of Greek ethnicity. It would be misguided to try to identify him with a single religious faith. His writings reflect a hybridization of pagan (Greco-Roman pagan, Egyptian pagan, etc.), Christian and Jewish faiths.
3 See Carl Jung’s Alchemical Studies, which also includes a translation of the relevant passages of Zosimus.
4 The Chemical Wedding of Christian Rosencruetz has also been tied to the so-called Rosicrucians, a quasi-mystical/political entity. See Francis Yates’ The Rosicrucian Enlightenment.
5 Alchemists, Mediums, and Magicians: Stories of Taoist Mystics, translated by Thomas Cleary 177.
6 Ibid., p. 183.
7 Ibid., p 61-62
8 Ibid., p 132
9 My atheist brother, as he QCs this, points out that the quantum physics argument is New Age nonsense. I tell him to let a person have her pretty ideas. On alchemists who were frauds as well as the alchemists’ contributions to science see From Alchemy to Chemistry by John Read and The Alchemists, by M. Caron and S. Hutin, translated by Helen Lane.