Wikipedia tells me that crocheting has only been documented from the 19th century onwards. This astounded me, as it seems to me that crocheting is a simpler technique than knitting and I therefore assumed it was much older. What's the lowdown on the history of crocheting?
One may think that crocheting should have been invented sooner, but we simply don't have any evidence dating back to before the 19th century. Crossovers exist, though. Danish nålebinding, dating as far back as 300 BC, which certainly predates crocheting, is a crossover between crocheting and knitting.
Research suggests that crochet probably developed most directly from Chinese needlework, a very ancient form of embroidery known in Turkey, India, Persia, and North Africa, which reached Europe in the 1700s and was referred to as "tambouring," from the French "tambour" or drum. Tambouring involved yarn loops pulled through fabric. By eliminating the fabric, crochet may have been born.
Note that crocheting involves more advantages than knitting and is considerably more sophisticated, as, if crocheted fabric breaks, the fabric itself will incur less damage than knitted fabric because of the nature of how each loop is supported by others; each loop in crocheted fabric is supported only by the loops by its sides, which are unlikely to come loose unless heavily stressed because of the complex looping of each stitch. In knitting, each stitch is supported by the corresponding stitch in the row above and it supports the corresponding stitch in the row below, meaning it will incur much greater damage if the fabric is broken.
Given this, it makes sense that crocheting is as recent as is currently believed. Crocheting is more advanced, and one can't imagine that there was great pressure to invent new ways to create fabric from yarn, as crocheting's predecessors did just fine.