I think that backup and restore are the most critical things for any database professional to master. Whether you're a professional DBA, a developer setting up a system, or a seasoned DBA, I would argue having your data safe is the primary task. Security comes next, then performance, availability, and a number of other tasks that could go in any order, but if we don't have a way to restore our data when hardware fails, we're in trouble. And given enough time, or enough difference pieces and parts, something will fail. If you can't restore a system when a problem occurs, that's what Grant would call an RGE.
Over the years companies have moved to many different technologies to handle backups. Tape was common early in my career, but all disk systems, with de-duplication capabilities have become popular. I really don't think about anything other than getting a second (or third) copy of data these days, so I can't speak to any particular way of managing backups. However, for SQL Server, I do want the option to set full, differential, and log backups based on my RPO and RTO requirements.
There seems to be a new trend for companies that I ran across: they're moving to the cloud. Here's a short slideshow of some stats that show cloud use is increasing. This is a survey, so it's not all companies, but the trends are clear. More data is being backed up, and it's likely easier (and cheaper) to use cold storage in the cloud. That makes sense since it's data that you expect you'll very rarely need to use in a restore.
There are a couple of other interesting items I saw in the survey. The number of companies that are backing up more than 100TB grew quite a bit, even as the number of companies backing up < 25TB fell. That's a sign that we're capturing more data. Whether we need to, or whether legislation like the GDPR will get companies to trim some of that data, remains to be seen.
Another interesting item is that more companies are testing their DR plans. Fewer never test them, but the frequency is increasing with more companies testing quarterly or monthly. That's smart as we become more dependent on computer systems. I know some organizations can't roll back to paper, as we've seen in a number of airline IT issues. If you never test your DR plan, I hope that you don't have an issue when you can ill afford to find another job, becuase you might suffer those consequences. Really, I hope that you actually know this isn't professional and you start working on ways to test a restore of service.
More companies are moving to the cloud, and the resistance for security, cost, privacy, etc. reasons is going down. I think many of the concerns that both executives and IT professionals have had in the past are proving to be non-issues. This is especially true as more vendors institute government rated or more secure data centers as a part of their product offering.
If you don't like the cloud, that's fine. If you don't know anything about it except rumor, guesses, or hearsay, I'd suggest you learn more. The cloud is likely coming into your career, so learn a bit about it. At least enough to give reasons why you don't want to move your data there. If you do, you might be surprised that the cloud is not that bad a place to be, at least for some workloads.