Some developments on fractional Fourier optics are reported in this paper. First, a thick lens can be regarded as a fractional Fourier transformer. Second, relations between the Collins formulae and the fractional Fourier transform or fractional Hankel transform are bridged, we show that the Collins formulae in spatial domain or in spatial-frequency domain can be described by the fractional Fourier transform or fractional Hankel transform. Third, connections between the multi-element resonators and the scaled fractional Fourier transforms are established, it is shown that there exists twice scaled fractional Fourier transform for beams in completing one round trip, the beam oscillation in resonator can be viewed as a process of consecutive implementing scaled fractional Fourier transform. Finally, some extensions of the fractional Fourier transforms to misaligned optical systems are simply reviewed.