What is the name of Microsoft's email service that replaced Hotmail?

Microsoft's email service that replaced Hotmail is Outlook.com.

Outlook.com is Microsoft's web-based personal email service and the successor to Hotmail. Microsoft introduced the Outlook.com name in July 2012, then completed the transition from Hotmail in May 2013. Existing users could keep their Hotmail addresses, while new accounts could use the outlook.com domain.

The service offers more than email. A Microsoft account can connect Outlook.com with calendars, contacts, tasks, cloud services, and other Microsoft products. Outlook.com is accessed through a browser and is also available through mobile apps and standard email clients using supported protocols.

Hotmail itself began in 1996, founded by Sabeer Bhatia and Jack Smith, and Microsoft acquired it in 1997. It later passed through names including MSN Hotmail and Windows Live Hotmail. A common confusion is between Outlook.com and Microsoft Outlook: Outlook.com is the consumer webmail service, while Microsoft Outlook is also the name of desktop and mobile email software used with personal, school, and workplace accounts.