This paper reports on ongoing work on a large sample of bahuvrihi compounds in English and Spanish. After a brief characterization of bahuvrihi compounds, distinguishing them from a similar type of exocentric compounds (V+O compounds), the goal of the paper is clearly stated, namely to answer a number of questions, especially these two: (a) Does the metonymy CHARACTERISTIC PROPERTY FOR CATEGORY motivate the exocentric nature of all the compounds in the sample?; (b) Are other metonymies or metaphors also involved? If so, which are the metonymic or metaphoric patterns observable in conceptualizations underlying these compounds? The bulk of the paper is devoted to the detailed conceptual analysis of a large set of representative bahuvrihis in both languages. The results show that the above metonymy is responsible for the exocentric nature of all the compounds in the sample and that the characteristic property mapped by that metonymy is conceptualized in one of these three ways: literally, metonymically or metaphorico-metonymically. These three conceptualization patterns constitute the three major types of bahuvrihis in both languages; various further subtypes are proposed for each type. The paper ends with some tentative remarks on the Cognitive Grammar representation of the semantic structure of these compounds, on the connection between their semantic structure and their grammar and prosody, on a blending account of these lexemes, and on the contrasts identified between both languages.