Magnetic field sensors are an integral part of many industrial and biomedical applications, and their utilization continues to grow at a high rate. The development is driven both by new use cases and demand like internet of things as well as by new technologies and capabilities like flexible and stretchable devices. Magnetic field sensors exploit different physical principles for their operation, resulting in different specifications with respect to sensitivity, linearity, field range, power consumption, costs etc. In this review, we will focus on solid state magnetic field sensors that enable miniaturization and are suitable for integrated approaches to satisfy the needs of growing application areas like biosensors, ubiquitous sensor networks, wearables, smart things etc. Such applications require a high sensitivity, low power consumption, flexible substrates and miniaturization. Hence, the sensor types covered in this review are Hall Effect, Giant Magnetoresistance, Tunnel Magnetoresistance, Anisotropic Magnetoresistance and Giant Magnetoimpedance.