The extreme conditions found in and around pulsars make them fantastic natural laboratories, providing insights to a rich variety of fundamental physics and astronomy. To discover more pulsars we have begun the High Time Resolution Universe (HTRU) survey: a blind survey of the northern sky with the 100-m Effelsberg radio telescope in Germany and a twin survey of the southern sky with the 64-m Parkes radio telescope in Australia. The HTRU is an international collaboration with expertise shared among the MPIfR in Germany, ATNF/CASS and Swinburne University of Technology in Australia, University of Manchester in the UK and INAF in Italy. The HTRU survey uses multi-beam receivers and backends constructed with recent advancements in technology, providing unprecedentedly high time and frequency resolution, allowing us to probe deeper into the Galaxy than ever before. While a general overview of HTRU has been given by Keith at this conference, here we focus on three further aspects of HTRU discoveries and highlights. These include the ‘Diamond-planet pulsar’ binary J1719-1438 and a second similar system recently discovered. In addition, we provide specifications of the HTRU-North survey and an update of its status. In the last section we give an overview of the search for highly-accelerated binaries in the Galactic plane region. We discuss the computational challenges arising from the processing of the petabyte-sized HTRU survey data. We present an innovative segmented search technique which aims to increase our chances of discovering highly accelerated relativistic binary systems, potentially including pulsar-black-hole binaries.