I will talk about the problem of decoding a topological code, that consists of identifying the optimal recovery operation given the syndrome of an error, or equivalently of inferring the most likely world-line homology given a defect configuration. I will describe a new decoding algorithm [Phys. Rev. Lett. 104 050504 arXiv:0911.0581 and arXiv:1006.1362] for Kitaev's toric code (KTC) that runs in a time proportional to the log of the number of particles, an improvement over the previously known polynomial-time decoding algorithm. This algorithm also achieves a higher threshold on the depolarizing channel. Moreover, we have recently shown that all two dimensional topological stabilizer codes can be mapped onto each other by local transformations [arXiv:1103.4606, arXiv:1107.2707]. This local mapping enables us to use any decoding algorithm suitable for one of these codes to decode other codes in the same topological phase. We illustrate this idea with the topological color code that is found to be locally equivalent to two copies of KTC and we extend it to decode the topological subsystem color code.