Optical dispersion, the variation of the speed of light with frequency in a material, presents significant challenges in modern optical systems, including chromatic aberration and pulse signal distortion. Traditional approaches to dispersion engineering of an optical lens system require the use of a set of sub-lenses of opposite dispersion properties, largely increasing the overall lens thickness. Ultrathin metasurfaces offer unprecedented control over optical wavefronts with advanced functionalities. Developing achromatic metalenses has thereby emerged as a timely research topic for metasurface research. This Perspective article provides a comprehensive overview of dispersion engineering methods in metalenses, including the use of 2D and 3D meta-atoms fabricated from planar lithography and 3D laser lithography methods, respectively. We compare key figures of merit of achromatic metalenses developed for different wavelength ranges and discuss recent inverse design of large-scale achromatic metalenses. We believe advanced machine learning methods as well as hybrid nanofabrication of diffractive metalenses, refractive lenses, and metamaterials-like spaceplates could offer promising avenues for overcoming current challenges and eventually push ultrathin achromatic optics to practical applications in optics-related fields.