\indent consider a crystal formed of two types of atoms placed at the nodes of the integer lattice. the type of each atom is chosen at random, but the crystal is statistically shift-invariant. consider next an electron hopping from atom to atom. this electron performs a random walk on the integer lattice with randomly chosen transition probabilities (since the configuration seen by the electron is different at each lattice site). this process is highly non-markovian, due to the interaction between the walk and the environment. we will present a martingale approach to proving the invariance principle (i.e. gaussian fluctuations from the mean) for (irreversible) markov chains and show how this can be transferred to a result for the above process (called random walk in random environment). this is joint work with timo seppalainen.