"Strong and Weak Lensing with HST and High Redshift Galaxies: Recent Advancements": The science related to both strong and weak lensing has advanced significantly since (and much thanks to) the launch of the Hubble Space Telescope (HST) ~two decades ago, with acceleratingly interesting results in recent years such as the detection and study of high-redshift galaxies at z~10 and beyond, due to the magnification power of cosmic lenses such as galaxy clusters. In my talk I will review the strong and weak cluster lens modeling and related science, particularly with HST, with an emphasis on recent advancements . I will talk about our contribution to the field and present results from the Cluster Lensing And Supernova with Hubble (CLASH) and Hubble Frontier Fields programs, as well as other independent results, with an emphasis on high-redshift galaxies, and some expectations for the near future.