This review summarizes the status of three current efforts to develop optical gyroscopes with improved performance over state-of-the-art fiber optic gyroscopes (FOGs) in terms of accuracy, size, and/or cost. The first approach consists in replacing the temporally incoherent Er-doped fiber source used in FOGs withy a low-coherence laser whose linewidth is broadened to tens of GHz by an external phase modulator driven by noise. A FOG with a 3.24-km coil interrogated by such a source has recently produced a noise and a drift approaching strategic-grade performance, and exhibits a source mean-wavelength stability below 1 ppm. The second approach is the use of a hollow-core fiber (HCF) in the sensing coil of a FOG to reduce thermal drift. A FOG utilizing 250 m of polarization-maintaining HCF and interrogated with a broadened laser is shown to exhibit a noise of 0.135 deg/√h limited by backscattering arising from surface modes in the fiber, and a drift of 1.2 deg/h dominated by polarization coupling. The third investigation is an optical gyroscope made of two coupled ring resonators, one exhibiting loss and the other one gain, operated at or near an exceptional point. Time-domain simulations predict that when operated below threshold and interrogated with a conventional biasing and read-out scheme, this gyroscope exhibits a rotation sensitivity at least 170 times larger than an optimized single-ring resonator with the same radius (5 mm) and loss (0.5 dB). Such systems have a great potential for producing a new generation of gyroscopes with significantly smaller footprints than FOGs.