In the language of Einstein's theory of special relativity, a tachyon (provided one exists) is a particle with space-like four-momentum. If its energy and momentum are real, its rest mass is imaginary. It is doubtful if an imaginary mass is physically meaningful.
The proper time experienced by a tachyon is also imaginary.
A tachyon is constrained to the space-like portion of the energy-momentum graph. Therefore, it can never slow to light speed or below. Curiously, as its energy decreases, its velocity increases.
If tachyons exist and are allowed to interact with ordinary matter, causality could in principle be violated.
In the theory of general relativity, it is possible to construct spacetimes in which particles propagate faster than the speed of light, relative to a distant observer. One example is the Alcubierre metric. However, these are not tachyons in the above sense, as they do not exceed the speed of light locally.