In MySQL keys and constraints are used to assign a special index to a column, meaning that this column will be approached somehow different by the MySQL server; or in other terms it will be facilitated.

Here are the lists of MySQL indexes and constraints:

MySQL indexes

UNIQUES Assigned column's value has to be unique inside the database, or will be rejected
FULLTEXT Accepts only values that are of CHAR, VARCHAR or TEXT type. May be used only with MyISAM engine
SPATIAL Accepts only spatial columns. Used only with MyISAM engine and accepts no NULL values

MySQL keys and constraints

AUTO_INCREMENT Sets which column will have automatic increment with every new input. Usually same as PRIMARY KEY
CHARACTER SET Sets database's or table's character set in MySQL
CHECK Specifies condition when manipulating data inside s table
COLLATION Sets database's or table's collation
CONSTRAINT Sets or resets (drops) a constraint index applied to multiple columns.
ON DELETE CASCADE Deletes data from child tables
DEFAULT Inserts a default value into a column
FOREIGN KEY Used to link two tables by pointing its own table to the primary key of another one
IDENTITY Used in combination with AUTO_INCREMENT to define the starting number and step of increment
NOT NULL Makes sure that NULL values are nor allowed while inerting or updating rows of a particular column; NULL values refers to no value at all and it does not include empty spaces
PRIMARY KEY Uniquely identifies each record in a database table with the difference that one table may have only one PRIMARY KEY
REFERENCES Used with FOREIGN KEY specifying that the values of the referencing table (FOREIGN_KEY) are present in the referenced table too
UNIQUE Uniquely identifies each record in a database table