The limitations of silicon electronic devices increasingly constrain the performance of silicon integrated circuits (ICs) and their use in emerging applications. Next-generation devices with exceptional performance and new functionalities have been realized using two-dimensional materials such as graphene. For example, graphene Hall-effect sensors (GHSs) greatly outperform commercial silicon magnetic-field sensors and could significantly improve the performance of sensor arrays used in magnetic imagers and biosensing. However, the 2D nature of graphene leads to undesirable effects such as device heterogeneity, offset, and noise which limit the practical appeal of GHSs compared to silicon devices with poorer performance but higher reliability. This thesis investigates several techniques drawn from device, circuit, and system-level perspectives to address the existing limitations of graphene Hall sensors and enable their more widespread usage. A central theme of this work is combining graphene Hall sensors with silicon integrated circuits and using the standout aspects of silicon IC technology - reliability, high speed, and scalability - to mitigate the undesirable effects of GHSs while retaining their advantages. This thesis also explores the applications of GHSs for in-flow detection of magnetically labeled particles such as cells, which can be used to diagnose and monitor cancer and infectious diseases using unprocessed blood samples.