Direct ascent was notably featured in the 1950 science fiction film Destination Moon. In fact, before the Apollo program, direct ascent was how most lay people conceived of how a flight to the Moon would actually work.
The advantage of direct ascent is its simplicity, as it obviates the need for any rendezvous phases. The main, and largely insurmountable, disadvantage of direct ascent is that it requires an almost unfathomably massive spacecraft to make it work. NASA looked at a few different direct ascent spacecraft designs, but these were considered too large or unworkable.
Earth orbit rendezvous
Earth orbit rendezvous (EOR) was another pre-Apollo competing method conceived for getting to the Moon. The hallmark of EOR approaches was several launches of different spacecraft components into Earth orbit where assembly into a larger spacecraft could be performed. This larger spacecraft would then fly to the moon and land on it, later taking off and returning to Earth.
EOR has the advantage of allowing the tricky rendezvous phase of the mission to occur close to Earth. If trouble developed, astronauts could simply reenter the atmosphere and be rescued; if the rendezvous during an LOR mission failed, the moonwalkers would perish. NASA’s Gemini program convincingly proved that on-orbit rendezvous techniques worked and were safe and could be used for LOR approaches.
EOR’s disadvantages include its requirement that more than one rocket launch from Earth and that it generally sends more mass to the lunar surface — and is therefore less fuel efficient — than LOR.
The way of the future
NASA’s Artemis program, which aims to return humans to the surface of the Moon, centers on using the Space Launch System (SLS) rocket to launch an Orion crew capsule to conduct an LOR. In that sense, it’s similar to the mission profile used by Apollo.