Facebook isn't the only internet behemoth suffering from serious downtime. As of mid-day on July 3rd, Twitter is experiencing "some issues" with direct message delivery and notifications. We've asked Twitter if it can clarify what happened, but you probably won't be sliding into anyone's DMs until the issue is resolved.
Twitter isn't a stranger to technical problems (many still have memories of the fail whale), but they've more recently revolved around strange behavior rather than full-fledged outages. That makes the DM failure all the more glaring -- as much as Twitter's reliability has improved over the years, it's still not immune to issues like this.
We're currently having some issues with DM delivery and notifications. We're working on a fix and will follow up as soon as we have an update for you. Apologies for the inconvenience.— Twitter Support (@TwitterSupport) July 3, 2019