Factors related to the requirements engineering process and customers have been repeatedly reported among those that most strongly influence the success of a software project. However, requirements engineering research has so far barely studied practice from a customer-based perspective. Furthermore, rigorous evidence about customers' perspectives regarding requirements engineering approaches is scarce, and links between customer-based requirements engineering research and the industrial practices are necessary. This paper argues that new research is necessary to tackle the above weaknesses. Our position is that: requirements specification approaches must be validated from a customer-based perspective; the influence of customers' characteristics on the requirements engineering process must be studied in more depth; and potential customer-based improvements in practice must be assessed. We also present situations in which the results from these activities would help practitioners, propose a research agenda to execute these activities, and discuss challenges that might hinder their execution.