Traditional objective lenses based on refraction of light are quite critical in modern microscopy but the focusing and imaging resolutions are diffraction-limited to be half a wavelength. Recently, through manipulating diffraction of light with binary masks or gradient metasurfaces, many miniaturized and planar lenses have been reported with intriguing functionalities such as ultra-high numerical aperture (NA), long focal length, large depth of focus and a diffraction-limit-broken spot for far-field, non-invasive, label-free and super-resolution imaging.  Here I introduce the recent advances in planar diffractive lenses (PDLs) from the viewpoint of a united theory “diffraction-based focusing optics”, reveal the underlying physics in their fighting against the diffraction limit via constructive or destructive interference, and redefine the new diffraction limit of PDLs to be 0.38λ/NA (λ is the wavelength). Various approaches of realizing PDLs are introduced in terms of their unique performances and rechecked by using optical aberration theory. A detailed tutorial about applying PDLs in nano-imaging and nano-fabrication will be provided.