Allusions happen when an author indirectly refers to another person or thing outside of the author's own literary work. The reference can be to a "person, place, thing or idea of historical, cultural, literary or political significance" (Literary Devices: Definition and Examples of Literary Terms, "Allusion"). It does not matter if what is referred to in an allusion is historical or fictional--an allusion can refer to either. An allusion can even be made through mentioning a name or stating a famous quote (Literary Devices: Literary Devices, Terms, and Elements, "Allusion"). Allusions can particularly be used as figures of speech by drawing analogies through the references in order to create more meaning and emotion.
Shakespeare commonly makes references to both Greek and Roman mythology in all of his plays, and we can consider these allusions because myths were written down by both the Greeks and Romans, making references to myths references to literary works. Also, any Greek or Roman gods or goddesses can be considered well-known mythological people.
We can see several very clear examples of allusions in the very first scene of Romeo and Juliet. When Lady Montague asks Benvolio, Romeo's cousin, if he has seen Romeo, Benvolio describes when he last saw Romeo at dawn, opening his description with an allusion to the sun god, called Helios by the Greeks and Apollo by the Romans:
Madam, an hour before the worshipp'd sun
Peer'd forth the golden window of the East,
A troubled mind drave me to walk abroad .... (I.i.114-16)
Since Benvolio uses the phrase "worshipp'd sun," we know he is referencing the sun god rather than speaking directly about the sun. Several other allusions to Roman mythology can also be seen throughout the rest of the scene.
But all so soon as the all-cheering sun
Should in the farthest East begin to draw
The shady curtains from Aurora's bed
This is an allusion to Aurora from Roman mythology.
She hath Dian's wit,
And, in strong proof of chastity well arm'd,
From Love's weak childish bow she lives uharm'd.
This is an allusion to Dian and Eros (Love) from Roman mythology.
Speak to my gossip Venus one fair word,
One nickname for her purblindson and heir,
Young Adam Cupid, he that shot so trim
When King Cophetua lov'd the beggar maid!
He heareth not, he stirreth not, be moveth not
This is an allusion to Venus and Cupid from Roman mythology.
Love is blind.
This is an allusion to Eros (Love) once again.