Converting monster types from 3.x to 5e

Aberrations
The definition of aberration has changed between 3.x and 5e. As of 5e, it only refers to monsters from the realms of chaos (e.g. Limbo, Far Realm). So any aberration that is literally an alien remains an aberration. Those which are merely strange are placed into another type: e.g. will-o-wisps are undead and naga are monstrosities. (Although I hate the monstrosity type, so in my house rules naga become dragons instead.)

Magical beast and monstrous humanoid
The magical beast and monstrous humanoid types have been deprecated. You might think they have been replaced by the monstrosity type, but this is not the case. Although many are placed in monstrosity, several magical beasts and monstrous humanoids from 3.x have been classified as other types: e.g. stirge, blood hawk and giant eagle are beasts; pegasus and unicorn are celestial; fire snake and gargoyle are elemental; blink dog and hag are fey; aarakocra, grimlock, kuo-toa, jackalwere, sahuagin, thri-kreen, and quaggoth are humanoid. The new type should be determined on a case-by-case basis. (I personally hate the monstrosity type as a catchall because that encourages lazy design.)

Outsiders
The outsider type has been deprecated as of 5e and replaced with more clearly defined types including aberration, celestial, construct, elemental, fey, fiend and so forth. Sometimes the new type is easy to determine: demons, devils, rakshasa, etc are fiends, angels, archons, couatls, etc are celestials, proteans are aberrations, genies are elementals, etc. Note that some of the subtypes may need to be dropped, e.g. archons no longer exist in 5e being replaced by angels. Other types the type may be different that you expect because of changes in 5e cosmology: e.g. the eladrins/azatas and guardinals/agathions are now typed as fey.

Sometimes the new type is not easy to determine or there may not be a good equivalent. For example, the only type that seems applicable to kami would be fey. In another example, aeons and psychopomps seemingly have no appropriate type so the only choice would seem to be "monstrosity" because it exists to hold monsters that cannot fit into other types (which I think is stupid and indicates the type mechanic is broken and needs fixing). However, if you are using a simple Moorcockian chaos/order/balance alignment system rather than the retarded good/evil/whatever system, then aeons and psychopomps make sense as celestials since they defend the balance (which is good in Moorcockian cosmology, whereas law and chaos are evil).