This study, carried out in Chile, describes difficulties in the incorporation of employability as an objective in the training of psychologists. Prior research emphasized confusion of key actors about how to train and measure employability. To illustrate that confusion, we compared perspectives of university Psychology department heads and employers of their graduates. Semi-structured interviews revealed understandings of various elements in the employment process. The department heads began by describing the process and criteria they follow to design, operate and assess their programs. Employers described the skills they have looked for when hiring graduates. Where possible the study notes the match between university training objectives and employer preferences. The skills promoted by universities and employers match on only some dimensions. 'Employability' varies in meaning across actors, occupations, and contexts. At present, universities and employers have little understanding of what the other seeks to accomplish.