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Único vs. solo

Word practice demo
While both único and solo can translate to only in English, they are not interchangeable and have distinct meanings and grammatical functions. Único refers to uniqueness, while solo either means alone or acts as an adverb meaning just.

Único

B1
Único is an adjective that means unique or one of a kind. When translated as only, it signifies the only one in existence or in a specific context. As an adjective, it must agree in gender and number (única, únicos, únicas) with the noun it modifies.
Fue el único sobreviviente del accidente.
(He was the only survivor of the accident.)
Esta es una oportunidad única en la vida.
(This is a unique opportunity in life.)
Mi única hermana vive en Argentina.
(My only sister lives in Argentina.)
Estos son los únicos zapatos que me quedan bien.
(These are the only shoes that fit me well.)
Su talento para la música es verdaderamente único.
(His talent for music is truly unique.)

Solo

A1
Solo has two main uses. As an adjective, it means alone or lonely and changes to agree in gender and number (sola, solos, solas). As an adverb, it means only or just and is invariable. In its adverb form, solo is a synonym for solamente and can always be replaced by it.
A mi padre le gusta estar solo cuando lee.
(My father likes to be alone when he reads.)
Ella se siente muy sola en la nueva ciudad.
(She feels very lonely in the new city.)
Solo quiero un vaso de agua, por favor.
(I only want a glass of water, please.)
Los niños jugaron solos en el jardín toda la tarde.
(The children played alone in the garden all afternoon.)
No estoy enojado, solo un poco cansado.
(I'm not angry, just a little tired.)
Trabajo solo los fines de semana.
(I only work on weekends.)

Summary

In summary, use único (the only one, unique) when referring to something as one of a kind. Use solo as an adjective to mean alone or lonely. Use solo as an adverb to mean only or just. A simple trick: if you can replace the word with solamente (just/only), the correct choice is the adverb solo. If it means the single existing one, use the adjective único.