The present work is a survey on aircraft hybrid electric propulsion (HEP) that aims to present state-of-the-art technologies and future tendencies in the following areas: air transport market, hybrid demonstrators, HEP topologies applications, aircraft design, electrical systems for aircraft, energy storage, aircraft internal combustion engines, and management and control strategies. Several changes on aircraft propulsion will occur in the next 30 years, following the aircraft market demand and environmental regulations. Two commercial areas are in evolution, electrical urban air mobility (UAM) and hybrid-electric regional aircraft. The first one is expected to come into service in the next 10 years with small devices. The last one will gradually come into service, starting with small aircraft according to developments in energy storage, fuel cells, aircraft design and hybrid architectures integration. All-electric architecture seems to be more adapted to UAM. Turbo-electric hybrid architecture combined with distributed propulsion and boundary layer ingestion seems to have more success for regional aircraft, attaining environmental goals for 2030 and 2050. Computational models supported by powerful simulation tools will be a key to support research and aircraft HEP design in the coming years. Brazilian research in these challenging areas is in the beginning, and a multidisciplinary collaboration will be critical for success in the next few years.