Realizing the physics programs of the planned and upgraded high-energy physics (HEP) experiments over the next 10 years will require the HEP community to address a number of challenges in the area of software and computing. For this reason, the HEP software community has engaged in a planning process over the past two years, with the objective of identifying and prioritizing the research and development required to enable the next generation of HEP detectors to fulfill their full physics potential. The aim is to produce a Community White Paper which will describe the community strategy and a roadmap for software and computing research and development in HEP for the 2020s. The topics of event reconstruction and software triggers were considered by a joint working group and are summarized together in this document.