List of Stored Procedures/Functions Mysql Command Line

SHOW PROCEDURE STATUS;
SHOW FUNCTION STATUS;

show procedure status

will show you the stored procedures.

show create procedure MY_PROC

will show you the definition of a procedure. And

help show

will show you all the available options for the show command.

A more specific way:

SHOW PROCEDURE STATUS 
WHERE Db = DATABASE() AND Type = 'PROCEDURE'

use this:

SHOW PROCEDURE STATUS;

If you want to list Store Procedure for Current Selected Database,

SHOW PROCEDURE STATUS WHERE Db = DATABASE();

it will list Routines based on current selected Database

UPDATED to list out functions in your database

select * from information_schema.ROUTINES where ROUTINE_SCHEMA="YOUR DATABASE NAME" and ROUTINE_TYPE="FUNCTION";

to list out routines/store procedures in your database,

select * from information_schema.ROUTINES where ROUTINE_SCHEMA="YOUR DATABASE NAME" and ROUTINE_TYPE="PROCEDURE";

to list tables in your database,

select * from information_schema.TABLES WHERE TABLE_TYPE="BASE TABLE" AND TABLE_SCHEMA="YOUR DATABASE NAME";

to list views in your database,

method 1:

select * from information_schema.TABLES WHERE TABLE_TYPE="VIEW" AND TABLE_SCHEMA="YOUR DATABASE NAME";

method 2:

select * from information_schema.VIEWS WHERE TABLE_SCHEMA="YOUR DATABASE NAME";

As of MySQL 8.0, the mysql.procs table has been removed. Running any of the commands from answers here that use this table will yield you an error that says (quite logically):

Table 'mysql.proc' doesn't exist

Instead, to retrieve a list of only the names of procedures/functions, use:

SELECT specific_name FROM `information_schema`.`ROUTINES` WHERE routine_schema='<your_db_name>';

In my case, I edited it to show only the procedures and not the functions:

SELECT specific_name FROM `information_schema`.`ROUTINES` WHERE routine_schema='<your_db_name>' AND routine_type='PROCEDURE';

My favorite rendering of the procedures list of the current database: name, parameters list, comment

SELECT specific_name AS name, param_list AS params, `comment`
FROM mysql.proc
WHERE db = DATABASE()
AND type = 'PROCEDURE';

Add returns for functions:

SELECT specific_name AS name, param_list AS params, `returns`, `comment`
FROM mysql.proc
WHERE db = DATABASE()
AND type = 'FUNCTION';

List user's procedures and functions for all databases:

SELECT 
    `ROUTINE_SCHEMA` AS `database`
    ,`ROUTINE_TYPE` AS `type`
    ,`SPECIFIC_NAME` AS `name`
    ,`DTD_IDENTIFIER` AS `data_type`
FROM 
    `INFORMATION_SCHEMA`.`ROUTINES`
WHERE
  `definer` LIKE
  CONCAT('%', CONCAT((SUBSTRING_INDEX((SELECT user()), '@', 1)), '%'))
ORDER BY
    `database`
    ,`type`
    ,`name`
;

List user's procedures and functions for the database in use:

SELECT 
    `ROUTINE_SCHEMA` AS `database`
    ,`ROUTINE_TYPE` AS `type`
    ,`SPECIFIC_NAME` AS `name`
    ,`DTD_IDENTIFIER` AS `data_type`
FROM 
    `INFORMATION_SCHEMA`.`ROUTINES`
WHERE
  `definer` LIKE
  CONCAT('%', CONCAT((SUBSTRING_INDEX((SELECT user()), '@', 1)), '%'))
AND
   `ROUTINE_SCHEMA` = DATABASE()
ORDER BY
    `type`
    ,`name`
;