Phylogenetics has been central to the genomic surveillance, epidemiology and contact tracing efforts during the COVD-19 pandemic. But the massive scale of genomic sequencing has rendered the pre-pandemic tools inadequate for comprehensive phylogenetic analyses. Here, we discuss the phylogenetic package that we developed to address the needs imposed by this pandemic. The package incorporates several pandemic-specific optimization and parallelization techniques and comprises four programs: UShER, matOptimize, RIPPLES and matUtils. Using high-performance computing, UShER and matOptimize maintain and refine daily a massive mutation-annotated phylogenetic tree consisting of all SARS-CoV-2 sequences available in online repositories. With UShER and RIPPLES, individual labs - even with modest compute resources - incorporate newly-sequenced SARS-CoV-2 genomes on this phylogeny and discover evidence for recombination in real-time. With matUtils, they rapidly query and visualize massive SARS-CoV-2 phylogenies. These tools have empowered scientists worldwide to study the SARS-CoV-2 evolution and transmission at an unprecedented scale, resolution and speed.