Alchemy has its rise in the high middle ages, and fades after about the Enlightenment. Not much is taken seriously through the 19th century, but there are those who have revived interest in it in the 20th century. It can be understood in a number of ways:
a. Proto-chemistry: Alchemy is often understood as investigation into the reactions and changes of matter. Paracelsus, the great Renaissance alchemist, had a lab and gives detailed discussions of ways to make gold from lower metals. The search was for the "philosopher's stone", the substance that would make the transformation possible. There is also medical alchemy, the making of medicines and the charting of the forces of the body such that balances may be restored and maintained. Each substance was assumed to have three parts, Salt, Sulphur, and Mercury, and these could be separated out of everything and recombined to give powerful medicines.
b. Symbolism: alchemy uses symbols widely. The symbols are often fluid. There's lots of animal symbolism, for instance.
c. Depth psychology: a variety of people in the 20th century have pointed out the psychological components of alchemy. Jung was very interested in this. His notions of a collective unconscious found alchemical symbols as a useful expression. Alchemy, for him, is a sea of collective archetypal images that can surface in our dreams.
d. Mysticism: alchemy has always had a spiritual and soul aspect to it. The ascent of mysticism has found expression in alchemy's symbols as well.
e. Physics and metaphysics: alchemy bears resemblance to the scientific concern for beauty, neatness, simplicity in theories. Sometimes the way of testing ideas in physics is just too difficult, and theories must be judged by internal criteria. This is not so different from alchemist's convictions about the inner workings of their theories.
It is worth noting that some of these interpretations come well after the fact, after the texts that are significant in alchemy. Fundamentally, it is about spiritual transformation. The other senses emerge as alchemical work gets brought into other agendas.