After I have built my postgres hosts using Vagrant, I’m doing the following tests in order to check my replication:

pg_stat_replication view

Run the following statement on the master / primary host:

postgres=# SELECT * FROM pg_stat_replication;
   pid  | usesysid |  usename   | application_name | client_addr |       client_hostname        | client_port |         backend_start         | backend_xmin |   state   | sent_lsn  | write_lsn | flush_lsn | replay_lsn | write_lag
 | flush_lag | replay_lag | sync_priority | sync_state
 -------+----------+------------+------------------+-------------+------------------------------+-------------+-------------------------------+--------------+-----------+-----------+-----------+-----------+------------+-----------
 +-----------+------------+---------------+------------
  19382 |    16384 | replicator | walreceiver      | 192.168.0.3 | postgres-standby.localdomain |       48955 | 2019-01-07 12:04:26.588984+00 |              | streaming | 0/4000000 | 0/4000000 | 0/4000000 | 0/4000000  |
 |           |            |             0 | async
 (1 row)
 postgres=#

This view offers a lot of interesting information:

pid: Process id of walsender process
usesysid: OID of user which is used for Streaming replication.
usename: Name of user which is used for Streaming replication
application_name: Application name connected to master
client_addr: Address of standby/streaming replication
client_hostname: Hostname of standby.
client_port: TCP port number on which standby communicating with WAL sender
backend_start: Start time when SR connected to Master.
state: Current WAL sender state i.e streaming
sent_lsn: Last transaction location sent to standby.
write_lsn: Last transaction written on disk at standby
flush_lsn: Last transaction flush on disk at standby.
replay_lsn: Last transaction flush on disk at standby.
sync_priority: Priority of standby server being chosen as synchronous standby
sync_state: Sync State of standby (is it async or synchronous). 

WAL sender/receiver processes running on the servers.

On Master / Primary:

[Mon Jan 07 12:34:28 postgres@postgres-primary:~ ] $ ps aux |grep postgres

postgres 19382  0.0  0.5 397088 10516 ?        Ss   12:04   0:00 postgres: wal sender process replicator postgres-standby.localdomain(48955) streaming 0/4000000

root     19430  0.0  0.4 241076  7784 pts/0    S    12:21   0:00 sudo su - postgres

root     19432  0.0  0.2 191936  4648 pts/0    S    12:21   0:00 su - postgres

postgres 19433  0.0  0.1 115448  3468 pts/0    S    12:21   0:00 -bash

postgres 19475  0.0  0.2 155372  3996 pts/0    R+   12:34   0:00 ps aux

postgres 19476  0.0  0.1 112724  2404 pts/0    S+   12:34   0:00 grep --color=auto postgres

postgres 31163  0.0  1.2 396244 22984 ?        S    08:10   0:00 /usr/pgsql-10/bin/postgres -D /test03/pgdata/data

postgres 31164  0.0  0.2 249048  5108 ?        Ss   08:10   0:00 postgres: logger process

postgres 31166  0.0  0.6 396244 10908 ?        Ss   08:10   0:00 postgres: checkpointer process

postgres 31167  0.0  0.2 396244  5000 ?        Ss   08:10   0:00 postgres: writer process

postgres 31168  0.0  0.5 396244 10324 ?        Ss   08:10   0:00 postgres: wal writer process

postgres 31169  0.0  0.4 396660  8368 ?        Ss   08:10   0:00 postgres: autovacuum launcher process

postgres 31170  0.0  0.2 251168  4168 ?        Ss   08:10   0:00 postgres: archiver process   last was 000000010000000000000003

postgres 31171  0.0  0.3 251168  5520 ?        Ss   08:10   0:00 postgres: stats collector process

postgres 31172  0.0  0.4 396536  7316 ?        Ss   08:10   0:00 postgres: bgworker: logical replication launcher

[Mon Jan 07 12:34:32 postgres@postgres-primary:~ ] $

On Standby / Slave:

[Mon Jan 07 12:23:33 vagrant@postgres-standby:~ ] $ ps aux |grep postgres
 vagrant  19073  0.0  0.1 112720  2408 pts/0    S+   12:34   0:00 grep --color=auto postgres
 postgres 30580  0.0  1.2 396244 22608 ?        S    12:04   0:00 /usr/pgsql-10/bin/postgres -D /test03/pgdata/data
 postgres 30581  0.0  0.2 249048  5108 ?        Ss   12:04   0:00 postgres: logger process
 postgres 30582  0.0  0.3 396340  6956 ?        Ss   12:04   0:00 postgres: startup process   recovering 000000010000000000000003
 postgres 30584  0.0  0.2 396244  5000 ?        Ss   12:04   0:00 postgres: checkpointer process
 postgres 30585  0.0  0.2 396244  5064 ?        Ss   12:04   0:00 postgres: writer process
 postgres 30586  0.0  0.2 251168  4232 ?        Ss   12:04   0:00 postgres: stats collector process
 postgres 30594  0.0  0.5 403380  9576 ?        Ss   12:04   0:01 postgres: wal receiver process   streaming 0/4000000
 [Mon Jan 07 12:34:39 vagrant@postgres-standby:~ ] $

One way of checking how up to date is our replication is by checking the amount of WAL records generated in the primary, but not yet applied in the standby.

On Primary / Master:

[Mon Jan 07 12:34:48 postgres@postgres-primary:~ ] $ psql
 psql (10.6)
 Type "help" for help.
 postgres=# SELECT pg_current_wal_lsn();
  pg_current_wal_lsn
 0/4000000
 (1 row)
 postgres=#

On Standby / Slave:

 [Mon Jan 07 12:37:19 postgres@postgres-standby:~ ] $ psql
 psql (10.6)
 Type "help" for help.
 postgres=# SELECT pg_last_wal_receive_lsn();
  pg_last_wal_receive_lsn
 0/4000000
 (1 row)
 postgres=#

postgres=# SELECT pg_last_wal_replay_lsn();
  pg_last_wal_replay_lsn
 0/4000000
 (1 row)
 postgres=#

We can use the following query to get the lag in seconds.

postgres=# SELECT CASE WHEN pg_last_wal_receive_lsn() = pg_last_wal_replay_lsn()
 postgres-# THEN 0
 postgres-# ELSE EXTRACT (EPOCH FROM now() - pg_last_xact_replay_timestamp())
 postgres-# END AS log_delay;
  log_delay
      0
 (1 row)
 postgres=#