This question is discussed by Stephen Kneale.

Do we look for Christ in all the psalms, or only in this customarily considered to be Messianic?

Expositors from Augustine to Luther tended to take the maximalist approach.  Calvin, however, stressed the original contexts of the psalms, and so adopted a more minimal interpretation.

In recent times, Bonhoeffer and Ash have leant towards the maximalist position, whereas others, including Dale Ralph Davis, incline towards a more limited reading.

What are some reasons for seeing Christ in many of the psalms – indeed, in the Psalter as a whole?

‘The righteous man’ in Psalm 1

The first two psalms may be regarded as together forming an introduction to the Psalter.

In Psalm 1, ‘the righteous’ is usually singular, whereas ‘the wicked’ are invariably plural.  This points us towards the truly righteous man who we meet in the Gospels.

Davidic authorship

Roughly half the psalms are attributed to David.  Other psalmists, such as Asaph, did their work under David’s direction (1 Chron 25:1f).  We should read the psalms, then, as penned by God’s anointed king, the representative of the nation, and forerunner of Christ himself.

Accordingly, we should read the imprecatory psalms not as expressions of personal vengeance, but as coming from David as the head of the nation.

New Testament quotations

It may be argued that New Testament quotations do not set limits on which psalms are Messianic, but rather demonstrate how we are to interpret the Psalter as a whole.

But what about confessions of sinfulness in the Psalms?  How can these be placed on the lips of the spotless Son of God?  Answer: just as it was ‘fitting’ for Jesus to stand in our place at his baptism (Mt 3:15), so, as our representative, he can sing the pentential psalms in our place.

The Psalms and the Cross

Think about what it would have meant for Jesus to have sung the psalms on his way to the cross:

‘Try it with Psalm 3—written by the Messianic king, betrayed and surrounded. Read (or better, sing!) verse 5, as many down the ages have done, speaking of the death and resurrection of that Messianic king.’