We have well over a dozen blackcurrant bushes on our plots and as they are now 4 years old it was time to take out some of the oldest wood to keep the bushes fruiting well and full of vigour. The old wood is taken out right down to the ground.
One thing to be well aware of is big bud disease. This is shown in the middle picture, the bud being big and swolen compared to others on the bush. It is caused by mites which swell buds and come the spring, these mites invade surrounding growth imparting a revision virus which cause the bushes to become sickly and unproductive. Any signs of big bud should be pruned out and burned.
This pruning left a big pile of sticks, but before burning or composting I always take a load of cuttings which are great to plant in any spaces that appear or as gifts. You want to aim for straight-ish sticks about 12" long and as thick as a pencil. These cuttings can be plunged into a nursery bed, about half their length and left for a year, or as I do, plunged around a deep pot and left somewhere out of the way till they show signs of growth when they can be potted on individually. Most will strike they are that easy.