Is there a way to send emails when someone logs in?
A possible solution is to use the Rules module and create a custom rule like so:


Rules Event = After a user logs in.
Rules Action = Send an eMail.


That's really it (a kind of Rules 101 also if you want ...).

Here is a rule (in Rules import format) that should answer your question:

{ "rules_notify_about_login" : {
    "LABEL" : "Notify admin about login",
    "PLUGIN" : "reaction rule",
    "ACTIVE" : false,
    "OWNER" : "rules",
    "REQUIRES" : [ "rules" ],
    "ON" : { "user_login" : [] },
    "IF" : [
      { "NOT user_has_role" : { "account" : [ "account" ], "roles" : { "value" : { "3" : "3" } } } }
    ],
    "DO" : [
      { "mail" : {
          "to" : "[site:mail]",
          "subject" : "New login",
          "message" : "Some user just completed a login to [site:name], located at [site:url].",
          "language" : [ "" ]
        }
      }
    ]
  }
}


The rule will be triggered (Rules Event) right after login was completed. For any user who does not have the role that matches "role id = 3" (= Rules Condition), aka for any user who is not an administrator, it will send an appropriate eMail to the admin user of the site.

If you have the Rules UI enabled, you can just import the above rule. As an alternative just use the Rules UI to create a similar rule from scratch.

Some further refinements you may want to apply to the above sample rule:


Adapt the value (=3) of the role id to fit your needs or just omit the Rules Condition if you want to perform the Rules Action for any role. 
Include relevant info about the user who performed a login (using available tokens about that user).
Adapt the eMail subject and content to fit your needs.


PS: This answer applies to D7, though for D8 it should be similar.