Language learning aptitude is a hypothesized psychological construct that has been used to explain differences in how fast and how well people can acquire a second language (L2). It is generally assumed that language learning aptitude is a multidimensional phenomenon, meaning that it consists of sub-constructs that are not necessarily interrelated. Research on language aptitude and its relationship with language learning outcomes has been undertaken for at least 70 years but much still remains unknown about the nature of this construct. Key to understanding the effects of a hypothesized latent trait like language aptitude is to ensure that it can be meaningfully quantified, and also that whatever real world observations that the trait is supposed to be linked to (in this case, L2 acquisition) can be measured with sufficient accuracy. The present thesis set out to explore issues in the measurement of both language learning aptitude and its predicted outcome (L2 acquisition), specifically applied to a context in which the L2 is Swedish. The validity of an increasingly popular test of language aptitude, the LLAMA, was examined in detail and a test of Swedish receptive vocabulary for L2 learners (the SweLT) was developed with the aim of efficiently serving various research purposes, including the study of language aptitude effects. In addition, theoretical and methodological issues in the assessment of individual differences in second language acquisition were outlined. The results from the empirical studies suggest that the LLAMA suffers from imprecision but that it may still be useful in research if due care is given to the interpretation of the obtained test scores. For quick assessment of general proficiency in Swedish, the SweLT seems to be a promising candidate but further refinement of this test is called for. Finally, some possible implications of aptitude research are discussed, including future use of aptitude tests as practical tools for individual adaptation of educational programs for adult L2 learners of Swedish. The findings of this thesis make it clear that the LLAMA would not be suitable for this purpose.