This paper surveys existing techniques for meeting the time-bound requirements of time-sensitive applications in the Internet of Things (IoT). To provide the foundation for identifying and classifying relevant techniques, we present three sample time-sensitive IoT applications and their time-bound requirements, describe the main computation and network resources in IoT that can be used to process such applications, and identify the main challenges in meeting their time-bound requirements. Based on these, the paper presents a comprehensive literature review of existing techniques and tools that can help meet application-specific time-bound requirements in IoT. The paper also includes a gap analysis in existing research outcomes and proposes research directions for bridging the remaining research gaps in supporting time-sensitive IoT applications.