In this thesis, low temperature specific heat measurements on small (μg) single crystals of different superconducting and magnetic systems are presented. The device used in this work features a combination of high sensitivity and good accuracy over the temperature range 1-400 K and allows measurements in high magnetic fields. It consists of a stack of thin films deposited in the center of a Si3N4 membrane. A batch process for the production of up to 48 calorimeters from a 2" silicon wafer was developed in order to overcome the scarcity of devices and allow systematic investigations. With abundance of calorimeters, single crystals of three different systems were studied. Fe2P is the parent compound of a broad family of magnetocaloric materials. The first-order para- to ferromagnetic phase transition at TC = 216 K was investigated for fields H up to 2 T, applied parallel and perpendicular to the easy axis of magnetization c. Strikingly different phase contours were obtained depending on the field direction. In particular, for H perpendicular to c, two different ferromagnetic phases, with magnetization parallel and perpendicular to c are found. It was also possible to observe the superheating/supercooling states, the latent heat, and the structural change associated to the first-order transition. BaFe2(As1-xPx)2 is a member of the recently discovered iron-based high-temperature superconductors family. Crystals with three different compositions were measured to study the doping dependence of the superconducting properties in the overdoped regime (x > 0.30). The electronic specific heat at low temperatures was analyzed with a two band α model, which allows to extract the gap amplitudes and their weights. The degree of gap anisotropy was investigated from in-field measurements. Additional information on the system was obtained by a combined analysis of the condensation energy and upper critical field. URu2Si2, a heavy fermion material, was studied around and above the hidden-order temperature THO = 17.5 K. The origin of the hidden-order phase is still not understood. High-resolution specific heat data were collected to help clarify if any pseudogap state is seen to exist above THO. We found no evidence for any bulk phase transition above THO.