  Every real is computable from a Martin-Loef random real. This well known
result in algorithmic randomness was proved by Kucera and Gacs. In this survey
article we discuss various approaches to the problem of coding an arbitrary
real into a Martin-Loef random real,and also describe new results concerning
optimal methods of coding. We start with a simple presentation of the original
methods of Kucera and Gacs and then rigorously demonstrate their limitations in
terms of the size of the redundancy in the codes that they produce. Armed with
a deeper understanding of these methods, we then proceed to motivate and
illustrate aspects of the new coding method that was recently introduced by
Barmpalias and Lewis-Pye and which achieves optimal logarithmic redundancy, an
exponential improvement over the original redundancy bounds.
