We review our recent work on Yb-doped and hybrid-structured solid photonic bandgap fibers (Yb-HS-SPBGFs) for linearly-polarized fiber lasers oscillating in the small gain wavelength range from 1160nm to 1200nm. The stack-and-draw or pit-in-jacket method is employed to fabricate two Yb-HS-SPBGFs. Both of the fiber shows optical filtering property for eliminating ASE in the large gain wavelength range from 1030nm to 1130nm and enough high birefringence for maintaining linear polarization, thanks to the photonic bandgap effect and the induced birefringence of the hybrid structure. The fiber attenuation of the Yb-HS-SPBGF fabricated by the pit-in-jacket method is much lower than that of the Yb-HS-SPBGF fabricated by stack-and-draw method. Linearly-polarized single stage fiber lasers using Yb-HS-SPBGFs are also demonstrated. Laser oscillation at 1180nm is confirmed without parasitic lasing in the fiber lasers. High output power and high slope efficiency in linearly-polarized single-cavity fiber laser using the low-loss Yb-HS-SPGF fabricated by the pit-in-jacket method are achieved. Narrow linewidth, high polarization extinction ratio and high beam quality are also confirmed, which are required for high-efficient frequency-doubling. A compact and high-power yellow-orange frequency-doubling laser would be realized by using a linearly-polarized single-cavity fiber laser employing a low-loss Yb-HS-SPBGF.