when:
The day of the celebration of Corpus Domini (June)

where:
The solemn procession commences in Piazza Duomo at 5.00 pm

features:
The Bishop, riding an adorned white horse, parades the Blessed Sacrament (host) through the main streets of the City.
This is in remembrance of an ancient tradition which originated in the year 1254.

Link: more info and photos

when:
The first saturday of September

where:
All around the inner port. The procession begin at 7.00 pm

features:
This procession in celebration of the protectors of the city of Brindisi, St. Theodore of Amasea and Saint Lawrence from Brindisi.
The ceremony began in 1776.
The procession begins at the Aragon's Castle where relics and statues of the saints are paraded in boats all round the inner port. Many boats take part in this procession and from the port the statues are then paraded through the streets and taken to the cathedral.

Link:
more info and photos