This paper focuses on the dearth of language-processing research addressing Spanish heritage speakers in assimilationist communities. First, we review key offline work on this population, and we then summarize the few psycholinguistic (online) studies that have already been carried out. In an attempt to encourage more such research, in the next section, we review the various techniques that psycholinguists commonly use in studies of language processing. We restrict our review to approaches that should be within the reach of most researchers. In our final section, we provide points of departure for further psycholinguistic investigations into this population. We do this in the hope that, one day, we may be able to determine with some degree of certainty the challenges that this population of Spanish speakers faces when processing their first language online, in real time. (Contains 12 notes.)