Satellite Application Facility on Support to Operational Hydrology and Water Management (H-SAF) is a EUMETSAT (European Organisation for the Exploitation of Meteorological Satellites) program, designed to deliver satellite products of hydrological interest (precipitation, soil moisture and snow parameters) over the European and Mediterranean region to research and operations users worldwide. Six satellite precipitation algorithms and concomitant precipitation products are the responsibility of various agencies in Italy. Two of these algorithms have been designed for maximum accuracy by restricting their inputs to measurements from conical and cross-track scanning passive microwave (PMW) radiometers mounted on various low Earth orbiting satellites. They have been developed at the Italian National Research Council/Institute of Atmospheric Sciences and Climate in Rome (CNR/ISAC-Rome), and are providing operational retrievals of surface rain rate and its phase properties. Each of these algorithms is physically based, however, the first of these, referred to as the Cloud Dynamics and Radiation Database (CDRD) algorithm, uses a Bayesian-based solution solver, while the second, referred to as the PMW Neural-net Precipitation Retrieval (PNPR) algorithm, uses a neural network-based solution solver. Herein we first provide an overview of the two initial EU research and applications programs that motivated their initial development, EuroTRMM and EURAINSAT (European Satellite Rainfall Analysis and Monitoring at the Geostationary Scale), and the current H-SAF program that provides the framework for their operational use and continued development. We stress the relevance of the CDRD and PNPR algorithms and their precipitation products in helping secure the goals of H-SAF's scientific and operations agenda, the former helpful as a secondary calibration reference to other algorithms in H-SAF's complete mix of algorithms. Descriptions of the algorithms' designs are provided including a few examples of their performance. This aspect of the development of the two algorithms is placed in the context of what we refer to as the TRMM era, which is the era denoting the active and ongoing period of the Tropical Rainfall Measuring Mission (TRMM) that helped inspire their original development. In 2015, the ISAC-Rome precipitation algorithms will undergo a transformation beginning with the upcoming Global Precipitation Measurement (GPM) mission, particularly the GPM Core Satellite technologies. A few years afterward, the first pair of imaging and sounding Meteosat Third Generation (MTG) satellites will be launched, providing additional technological advances. Various of the opportunities presented by the GPM Core and MTG satellites for improving the current CDRD and PNPR precipitation retrieval algorithms, as well as extending their product capability, are discussed