This paper proposes to refer to the field of software engineering related to the life cycle of dialogue systems as Dialogue Systems Engineering, and surveys this field while also discussing its future directions. With the advancement of large language models, the core technologies underlying dialogue systems have significantly progressed. As a result, dialogue system technology is now expected to be applied to solving various societal issues and in business contexts. To achieve this, it is important to build, operate, and continuously improve dialogue systems correctly and efficiently. Accordingly, in addition to applying existing software engineering knowledge, it is becoming increasingly important to evolve software engineering tailored specifically to dialogue systems. In this paper, we enumerate the knowledge areas of dialogue systems engineering based on those of software engineering, as defined in the Software Engineering Body of Knowledge (SWEBOK) Version 4.0, and survey each area. Based on this survey, we identify unexplored topics in each area and discuss the future direction of dialogue systems engineering.