The Eureka band, 1955. Source. 

Having long rejoiced in the bands heard on the 2 glorious CDs Frozen brass ( Nepal, India, Indonesia, Philippines, Ghana, Surinam, Bolivia, Peru!), it’s high time for me to get a basic education on the brass bands of New Orleans. [1]

The early years
After the Civil War and Emancipation, black civilian bands began to emerge, their style inspired by both European-style military bands and the ring shout of African slaves at the Sunday gatherings in Congo square. Organised by labor unions, social aid and pleasure clubs (the Perseverance Benevolent and Mutual Aid Association was founded as early as 1783), they would perform on parades for feast days like Mardi Gras, and play hymns and dirges on funeral processions.

By the early 20th century, new instruments, sounds, and styles were transforming the musical landscape. Early groups included the Excelsior (1879–1931) and Camelia bands. Perhaps most celebrated is

• the Eureka brass band (wiki; YouTube topic) (1920–75); here’s a brief clip from 1951:

Excerpts from 1952 to 1963:

Some more footage:

and Westlawn dirge, 1961:

Since the 1960s
By the early 1960s, despite concerns that the tradition was in decline, New Orleans brass bands enjoyed a renaissance, gaining wider celebrity through tourism, heritagification, and touring. As new generations were trained, the stylistic spectrum broadened. Among the more traditional groups:

• the Young Tuxedo band (topic), 1958:

and

• the Original Liberty jazz band, founded by Michael White in 1981—here they are in a 2015 recording for Smithsonian Folkways:

• The Onward band, 1968:

• The Olympia band, led by Harold Dejan and Milton Batiste, was a major training ground.  Here they are in 1982:

• The Treme band (wiki; YouTube topic)—among a cast of musicians featuring in the HBO series Treme (2010–13):

• The Fairview Baptist Church Christian Marching Band (with Danny Barker), and its successor the Hurricane band, led to more innovative groups like
• the Dirty Dozen band:

The Soul rebels. Source.

and by the early 80s, groups were incorporating hip-hop and funk into their repertoire, like the Rebirth band,

• The Soul rebels, Let your mind be free (1994):

• and the Hot 8 (wiki; YouTube topic):

Moreover,

• the Original Pinettes are “the ONLY female brass band in the universe” (see e.g. this article in Ethnomusicology 2017); here’s their version of Amy Winehouse’s Valerie:

For more brass bands, besides Frozen brass, do explore the Balkan scene (under Musical cultures of east Europe), Brassed off, and even the bands accompanying saeta ritual songs in Andalucia; for China, e.g. the Shaanbei big band sound. See also, Trumpets, wind and brass bands, and A jazz medley.

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[1] Besides studies like

• William J. Schafer, Brass bands and New Orleans jazz (1977)
• Richard Knowles, Fallen heroes: a history of New Orleans brass bands (1996), and
• Mick Burns, Keeping the beat on the street: the New Orleans brass band renaissance (2006),

note e.g. the Hogan Archive, a CD series from Smithsonian Folkways (e.g. this), as well as articles here and here. This article leads to four videos (starting here) that make a succinct introduction, along with an outline of the style’s rhythmic foundations (NB this virtual exhibition, with great photos and audio reminiscences). 

Wiki articles include
https://en.wikipedia.org/wiki/Jazz_funeral
https://en.wikipedia.org/wiki/Ring_shout
https://en.wikipedia.org/wiki/Brass_band#New_Orleans
https://en.wikipedia.org/wiki/Second_line_(parades)
https://en.wikipedia.org/wiki/Mardi_Gras_in_New_Orleans.
See also
https://beyondthedash.com/blog/cultural-spotlight/jazz-funerals-a-new-orleans-goodbye/7363.