Quantum computers may provide efficient solution to some computational problems that otherwise appear intractable, such as factoring of large integers. Unfortunately, the physical realization of this possibility has proved extremely difficult. Any reasonable implementation of a quantum computer must store qubits (i.e., quantum bits) in an encoded form so that to protect them from decoherence and other ``errors''; a computer built of bare qubits will not scale. On the other hand, logical qubits may be encoded directly into a system of many spins or electrons. In particular, three is a class of two-dimensional systems that carry anyons -- quasiparticles with unusual statistics. Some more exotic variety on anyons are called ``non-Abelian''. With two non-Abelian anyons trapped in potential wells far apart from each other, one obtains a system with several quantum states. There is virtually no way to change one state to another or to tell them apart until the anyons are brought together and fuse. Thus the states are protected from decoherence. I will discuss general properties of anyons as well as their potential use in quantum computation.