Blackcurrant bushes need constant renewal to ensure heavy crops. Older branches will bear fruit, but quantity and quality decline with age.
For this reason new bushes are planted deeply so that the plant produces vigorous young branches annually from below ground.
These are then used to replace older ones cut out after harvest.
Each year remove about one third of the oldest stems - the bark is very dark to the point of being black - and any that are weak or very low.
Always cut back to ground level or to a strong new shoot.
You can combine pruning with picking the fruit, or wait until winter.
Snipped from the BBC gardening site, (explains it far better than I can)

Time flies like an arrow; vinegar flies like an uncovered wine must.