Large software companies strive to make their engineering processes fast, and agile development has been a key enabler for flexible delivery of solutions following the market needs. In this context, continuous software engineering (CSE) has emerged as a way to iteratively develop software using practices that encompass business strategy, development, and operations that are aligned with the agile methodology. However, these practices can also lead to the accumulation of technical debt (TD), which has shown to be harmful to the software in the long-term. Due to its impact, TD should be managed in the context of CSE. However, to the best of our knowledge, there is a lack of an overview of how TD has been addressed in this context. In this study, we present the state of the art of TD in CSE; for this, we scrutinized the literature and found 41 studies. Our main findings show that this field of study is relatively new, with active participation of the industry, and that most CSE activities are not addressing TD yet; therefore, presenting a number of opportunities for future research.