Traditional machine learning algorithms rely on the assumption that the labeled and unlabeled data samples at hand are drawn from the same distribution. However, in many practical data analysis problems, one may have many labeled training samples belonging to a data domain, while the unlabeled samples one would like to classify may have different statistics. Domain adaptation methods aim to make use of the label information that is sufficiently available in a source domain for inferring the label information in a target domain where labels are much more scarce. In many data analysis problems, the data conforms to a low-dimensional model, or it may even be described solely through the pairwise affinities between the data samples, such as in social or communication networks. Graph models provide very convenient tools for such problems. In this talk, we will discuss the problem of domain adaptation on graphs. We will begin with an overview of the recent field of graph signal processing; in particular, how classical frequency analysis techniques can be extended to graph domains where the irregularity of the domain is the main challenge. We will then consider the problem of estimating a label function on a target graph with very few available observations, given a source graph where label observations are more easily available. Assuming that the spectrum, i.e., the frequency content, of the label function has similar characteristics over the source and the target graphs, we will discuss how the spectral content of the label function can be learnt from the source graph, and transferred to the target graph for more accurate inference.