The apostrophe is the most commonly misused punctuation mark. There are two uses for apostrophes:

Contractions are words where one or more letters have been omitted. The apostrophe is used in place of the letter(s) removed. Some of the most common examples are:

Contractions (it's, we'll, etc.) should not be used in academic essays.

Some words feature an apostrophe because they were once contracted, but now we only ever use the contracted form:

Possessives indicate that something belongs to someone. The place of the apostrophe depends on whether the possessor is singular or plural. A singular possessive apostrophe goes before the possessive 's'; a plural possessive apostrophe goes after the possessive 's'.

Some people find it useful to think of the singular possessive as:
and the plural possessive as:
This helps because, just as the apostrophe in a contraction shows that a letter has been left out, so the apostrophe in possessives shows that the words 'his' 'her' 'its' or 'their' have been left out. In other words, thinking in this way makes it clear that apostrophes always stand in for something that's missing. Understanding this means you'll never get an apostrophe wrong again.

There are some things to look out for: for example, plurals that don't end in 's',
e.g. 'children' and 'people', should have the possessive apostrophe placed before the possessive 's'.

N. B. the possessive 'its'

The possessive 'its' causes endless confusion with apostrophes. ‘Its’ is the possessive for ‘it’:

Just remember that like 'his' and 'hers', when 'its' is being used in the possessive sense, it never takes an apostrophe. 'Its' takes an apostrophe only when it's a contraction:

Tips:

1. Plain plurals, i.e. plurals simply denoting more than one, NEVER need apostrophes.

2. When referencing a multi-author work, e.g. Kernohan et al., phrase your sentence to avoid the possessive 's'. This is because et al. is Latin for 'et alii' which means 'and others'. To mix a Latin abbreviation with English punctuation looks odd, so don't write

instead write

The incorrect use of apostrophes shows poor attention to detail, something that no chemist wants to advertise.

1 adapted from Schenk, W. A., Dalton Transactions, 2011, 40, 1209-1219