Devanagari is part of the Brahmic family of scripts of India, Nepal, Tibet, and South-East Asia. It is a descendant of the 3rd century BCE Brahmi script through the Gupta script, along with Siddham and Sharada. Variants of script called Nāgarī, recognisably close to Devanagari, are first attested from the 1st century CE Rudradaman inscriptions in Sanskrit, while the modern standardised form of Devanagari was in use by about 1000 CE. Medieval inscriptions suggest widespread diffusion of the Nagari-related scripts, with biscripts presenting local script along with the adoption of Nagari scripts. For example, the mid 8th-century Pattadakal pillar in Karnataka has text in both Siddha Matrika script, and an early Telugu-Kannada script; while, the Kangra Jvalamukhi inscription in Himachal Pradesh is written in both Sharada and Devanagari scripts.
The 7th-century Tibetan king Srong-tsan-gambo ordered that all foreign books be transcribed into the Tibetan language. He sent his ambassador Tonmi Sambota to India to acquire alphabet and writing methods; returning with Sanskrit Nagari script from Kashmir corresponding to 24 Tibetan sounds and innovating new symbols for 6 local sounds. Other closely related scripts such as Siddham Matrka were in use in Indonesia, Vietnam, Japan and other parts of East Asia by between 7th- to 10th-century. Sharada remained in parallel use in Kashmir. An early version of Devanagari is visible in the Kutila inscription of Bareilly dated to Vikram Samvat 1049 (i.e. 992 CE), which demonstrates the emergence of the horizontal bar to group letters belonging to a word. One of the oldest surviving Sanskrit texts from the early post-Maurya period consists of 1,413 Nagari pages of a commentary by Patanjali, with a composition date of about 150 BCE, the surviving copy transcribed about 14th century CE.
Nāgarī is the Sanskrit feminine of Nāgara "relating or belonging to a town or city, urban". It is a phrasing with lipi ("script") as nāgarī lipi "script relating to a city", or "spoken in city".
The use of the name devanāgarī emerged from the older term nāgarī. According to Fischer, Nagari emerged in the northwest Indian subcontinent around 633 CE, was fully developed by the 11th-century, and was one of the major scripts used for the Sanskrit literature.
Most of the southeast Asian scripts have roots in the Dravidian scripts, except for a few found in south-central regions of Java and isolated parts of southeast Asia that resemble Devanagari or its prototype. The Kawi script in particular is similar to the Devanagari in many respects though the morphology of the script has local changes. The earliest inscriptions in the Devanagari-like scripts are from around the 10th-century, with many more between 11th- and 14th-century. Some of the old-Devanagari inscriptions are found in Hindu temples of Java, such as the Prambanan temple. The Ligor and the Kalasan inscriptions of central Java, dated to the 8th-century, are also in the Nagari script of North India. According to the epigraphist and Asian Studies scholar Lawrence Briggs, these may be related to the 9th-century copper plate inscription of Devapaladeva (Bengal) which is also in early Devanagari script. The term Kawi in Kawi script is a loan word from Kavya (poetry). According to anthropologists and Asian Studies scholars John Norman Miksic and Goh Geok Yian, the 8th-century version of early Nagari or Devanagari script was adopted in Java, Bali (Indonesia), and Khmer (Cambodia) around 8th or 9th-century, as evidenced by the many inscriptions of this period.