Widespread loss of genes on the Y is considered a hallmark of sex chromosome differentiation. Here we show that the initial stages of Y evolution are driven by massive amplification of distinct classes of genes. The neo-Y chromosome of Drosophila miranda initially contained about 3,000 protein-coding genes, but has gained over 3,200 genes since its formation about 1.5 million years ago primarily by tandem amplification of protein-coding genes ancestrally present on this chromosome. We show that distinct evolutionary processes may account for this drastic increase in gene number on the Y. Testis-specific and dosage-sensitive genes appear to have amplified on the Y to increase male fitness. A distinct class of meiosis-related multi-copy Y genes independently co-amplified on the X, and their expansion is probably driven by conflicts over segregation. Co-amplified X/Y genes are highly expressed in testis, enriched for meiosis and RNA interference functions and are frequently targeted by small RNAs in testis. This suggests that their amplification is driven by X versus Y antagonism for increased transmission, where sex chromosome drive suppression is probably mediated by sequence homology between the suppressor and distorter through the RNA interference mechanism. Thus, our analysis suggests that newly emerged sex chromosomes are a battleground for sexual and meiotic conflict.