How was a Linux machine traditionally joined to Active Directory, and what is used today?

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Accepted Answer

Earlier it was Samba with its Winbind service; today the recommended way is SSSD, usually set up with realmd.
Samba is the open-source project for working with Windows networks: Linux can use Windows file and print shares, and Samba can even act as a domain controller. For logon, Samba's Winbind service sat between Linux authentication (PAM) and AD. It used Kerberos to authenticate and LDAP to read users and groups, and it could also locate domain controllers and reset passwords via RPC.
SSSD (System Security Services Daemon) came out of the FreeIPA project. It talks to many identity providers (Active Directory, FreeIPA, OpenLDAP, 389 Directory Server) through one framework, caches identities and credentials so logon works offline, and plugs into PAM and NSS. realmd discovers the domain and writes the SSSD configuration for you.
Winbind is still around (it is needed when the Linux host itself serves Samba file shares to the domain). For a client that only needs AD logon, SSSD is the best practice.
Go deeper:

Wikipedia: Samba (software) — what Samba and Winbind provide.
 sssd.io — the SSSD project home, with docs for each provider.
 FreeIPA: About — the identity project SSSD grew out of.