The ability to monitor molecular targets is crucial in fields ranging from healthcare to industrial processing to environmental protection. Devices employing biomolecules to achieve this goal are called biosensors. Over the last half century researchers have developed dozens of different biosensor approaches. In this chapter we analyze recent advances in the biosensing field aiming at adapting these to the problem of continuous molecular monitoring in complex sample streams, and how the merging of these sensors with lab-on-a-chip technologies would be beneficial to both. To do so we discuss (1) the components that comprise a biosensor, (2) the challenges associated with continuous molecular monitoring in complex sample streams, (3) how different sensing strategies deal with (or fail to deal with) these challenges, and (4) the implementation of these technologies into lab-on-a-chip architectures.