This paper studies the use of structural representations for learning relations between pairs of short texts (e.g., sentences or paragraphs) of the kind: the second text answers to, or conveys exactly the same information of, or is implied by, the first text. Engineering effective features that can capture syntactic and semantic relations between the constituents composing the target text pairs is rather complex. Thus, we define syntactic and semantic structures representing the text pairs and then apply graph and tree kernels to them for automatically engineering features in Support Vector Machines. We carry out an extensive comparative analysis of state-of-the-art models for this type of relational learning. Our findings allow for achieving the highest accuracy in two different and important related tasks, i.e., Paraphrasing Identification and Textual Entailment Recognition.