Vector magnetometry in surveys for mineral exploration remains a challenge even with the highly sensitive magnetic field sensors that are currently available. Highly sensitive magnetometers such as Superconducting QUantum Interference Devices (SQUIDs) in mobile operation place a strong demand on the required dynamic range of the data acquisition system as it easily exceeds 24 bits. One solution to overcome this hurdle is to acquire gradiometry data. With this method, the spatial derivatives of the magnetic field vector, also called the magnetic gradient tensor, are measured. In this review, various sensor technologies are introduced, which allow for the design of sensors that measure individual magnetic gradient components. These sensors are called gradiometers and provide better information if the full gradient tensor is mapped during mineral exploration applications. There are already a number of full tensor magnetic gradiometers on the market which measure all components of the magnetic gradient. They are applied in mineral exploration, detection of UXO, and archaeology. The main focus of this work is on SQUID based gradiometry which enables the measurement of very weak magnetic gradients within the Earth’s magnetic field. Due to their ability to suppress a homogeneous magnetic field, the demands in terms of motion noise and dynamic range for field operation are relaxed compared to vector magnetometers. Using superconducting technologies various concepts for building gradiometers are available. Herein, low temperature superconducting planar-type first-order gradiometers will be introduced. They are 6 cm x 2 cm in size and have intrinsic noise floors of better than 50 fT/(m√Hz) down to 0.3 Hz. The highly symmetric SQUID gradiometers presented herein reduce the homogeneous part of the Earth’s field by at least a factor of 5,000. If the signals of a triple reference magnetometer are used, this homogeneous magnetic field is further reduced by a factor of better than 107 by using appropriate software algorithms. Full tensor measuring instruments were built using these gradiometers. They proved to be mechanically robust, reliable with low power consumption, easy to maintain and airworthy. The results of a test survey flown with the SQUID gradiometers are presented here and allow for a preliminary assessment of the exceptional performance of SQUID based full tensor gradiometry. Taking advantage of the unique properties of SQUIDs, in particular their periodic flux to voltage characteristics, enables new approaches for high-resolution vector magnetometers that are suitable for magnetic methods. Example developments will be introduced.