Narrow body and wide body aircraft are responsible for more than 75% of aviation greenhouse gas (GHG) emission and aviation, itself, was responsible for about 2.5% of all GHG emissions in the United States in 2018. This situation becomes worse when considering a 4-5% annual growth in air travel. Electrified aircraft is clearly a promising solution to combat the GHG challenge; thus, the trend is to eliminate all but electrical forms of energy in aircraft power distribution systems. However, electrification adds tremendously to the complexity of aircraft electric power systems (EPS), which is dramatically changing in our journey from conventional aircraft to more electric aircraft (MEA) and all electric aircraft (AEA). In this paper, we provide an in-depth discussion on MEA/AEA EPS: electric propulsion, distributed propulsion systems (DPS), EPS voltage levels, power supplies, and EPS architectures are discussed. Publications on power flow (PF) analysis and management of EPS are reviewed, and an initial schematic of a potential aircraft EPS with electric propulsion is proposed. In this regard, we also briefly review the components required for MEA/AEA EPS, including power electronics (PE) converters, electric machines, electrochemical energy units, circuit breakers (CBs), and wiring harness. A comprehensive review of each of the components mentioned above or other topics except for those related to steady state power flow in MEA/AEA EPS is out of this paper's scope and should be found somewhere else. At the close of the paper, some challenges in the path towards AEA are presented. Unless the discussed challenges are satisfactorily addressed and solved, arriving at an AEA that can properly operate over commercial missions will not be possible. INDEX TERMS aircraft electrification, all electric aircraft (AEA), electric power system (EPS), more electric aircraft (MEA), power distribution system, steady state power flow analysis.