Davydov was the son of a Jewish physician and amateur violinist, Yuly Petrovich Davidhoff from Courland Governorate.

This cello, now known as the Davidov Stradivarius, was owned by Jacqueline du Pré until her death and is currently on loan to cellist Yo-Yo Ma.

[3] Several composers dedicated works to him, notably Tchaikovsy's Cappricio Italien and Anton Arensky's first piano trio.

Davydov went on to write his still-popular "cello school" book of etudes and technique, completed in 1888, taking the physical limitations into considerations for advancing the possibilities in both the bow hand and playing in the high registers.

Another transcription album is a selection of Nocturnes and others solo piano works published by Edition Peters.