While magnesium diboride (MgB2) was first synthesized in the 1950s, MgB2’s superconductive properties were not discovered until 2001. It has the highest superconducting transition temperature of all the metallic superconductors at ~39 K at atmospheric pressure. MgB2 is also unique in that it has a two superconductive gaps, a pi gap at 2 meV and a sigma gap at 7.1 meV. There are a theoretical models discussing the inter- and intra- gap scattering of the superconductivity of MgB2 and the Josephson transport of MgB2 Josephson Junctions. The focus of this work is to further the study of all-MgB2 Josephson junctions and quantum interference device technology. This work discusses the transport in all-MgB2 Josephson junctions and designing, fabricating, and measuring multi-junction devices. The junctions studied include all-MgB2 sandwich-type Josephson junctions (one with TiB2 normal conducting barrier and another with an MgO insulating barrier). The junction MgB2 films were deposited by hyprid physical-vapor deposition and the junction barrier were deposited by sputtering. The junctions were patterned and etched with UV photolithography and argon ion milling. With the TiB2 barrier we studied Josephson transport by the proximity effect. With these junctions, we also observed complete suppression of the critical current by an applied magnetic field showing for the first time a leakage free barrier in an all-MgB2 Josephson junction with a single ultrathin barrier. We also studied junctions utilizing MgO barrier deposited by reactive sputtering which gave a larger characteristic voltage of 1-3 mV compared to TiB2 barriers. By connecting several SQUIDs with varying loop areas we developed of two types of superconducting quantum interference filters (SQIFs). The first SQIF designed with 21 SQUIDs connected in parallel and the SQUID loops are sensitive to magnetic fields applied parallel to the substrate. The SQUID loop areas were designed to vary in such a way that the voltage modulation gave a unique peak corresponding to the absolute value of the applied magnetic field. The SQIF shows an antipeak height of 0.25 mV with a transfer function of 16 V/T at 3 K. The lowest noise measured for this SQIF is 110 pT/Hz1/2. The second SQIF is designed with 17 SQUIDs in parallel and the SQUID loops are sensitive to magnetic field perpendicular to the substrate. This SQIF has shown improved voltage modulation with a peak height of 1 mV and a transfer function of 7800 V/T. The noise sensitivity was measured at 70 pT/Hz1/2. The sensitivity of the SQIF shows MgB2 potential superconductor to improve performance of current superconductive electronics. Utilizing known all-MgB2 junctions and SQUID parameters two rapid single flux quantum (RSFQ) circuits were designed and tested. A toggle flip flop (TFF) operating as a frequency divider was developed. The TFF design consisted of a Josephson transmission line, a splitter, and an interferometer (a DC SQUID). The TFF utilized an improved designed, compared to previous all-MgB2 TFFs, and showed operation up to 335 GHz at 7 K and operation up to 30 K. A low frequency set-reset flip flop (SRFF) was also developed to demonstrate RSFQ digital logic. The SRFF design includes a DC-SFQ converter, a Josephson transmission line, and an inductively coupled readout SQUID. The SRFF demonstrates proper digital logic by toggling between a high and low voltage state with a sequential set and reset input. While these developed devices are not close to the potential that MgB2 allows, they do show the promise MgB2 based devices have in making more sensitive and faster superconductive logic devices. / Physics