Genome sequences constitute the primary evidence on the origin and spread of the 2019-2020 Covid-19 pandemic. Rapid comparative analysis of coronavirus SARS-CoV-2 genomes is critical for disease control, outbreak forecasting, and developing clinical interventions. CoV Genome Tracker is a web portal dedicated to trace Covid-19 outbreaks in real time using a haplotype network, an accurate and scalable representation of genomic changes in a rapidly evolving population. We resolve the direction of mutations by using a bat-associated genome as outgroup. At a broader evolutionary time scale, a companion browser provides gene-by-gene and codon-by-codon evolutionary rates to facilitate the search for molecular targets of clinical interventions.