We have developed a high-throughput, microfluidics-based platform to perform kinetic analysis of viral infections in individual cells. We have analyzed thousands of individual poliovirus infections while varying experimental parameters, including multiplicity of infection, cell cycle, viral genotype, and presence of a drug. We make several unexpected observations masked by population-based experiments: (1) viral and cellular factors contribute uniquely and independently to viral infection kinetics; (2) cellular factors cause wide variation in replication start times; and (3) infections frequently begin later and replication occurs faster than predicted by population measurements. We show that mutational load impairs interaction of the viral population with the host, delaying replication start times and explaining the attenuated phenotype of a mutator virus. We show that an antiviral drug can selectively extinguish the most-fit members of the viral population. Single-cell virology facilitates discovery and characterization of virulence determinants and elucidation of mechanisms of drug action eluded by population methods.