DNA replication is the copying of DNA. It happens before the cell divides. The two DNA strands separate and DNA Polymerase reads the original DNA to insert complimentary nucleotides.
Transcription is the process of making RNA from a DNA template. This is done by the enzyme RNA polymerase.
Gene expression refers to all of the processes that are needed to produce a protein from DNA. It includes transcription, splicing (HL only) and translation.