For starters, you should be clear on when they expect a response back
If only recruiters and hiring managers took this seriously! They've been the worst communicators I've ever experienced in my professional life--as the applicant. I'm cool with ignorance of an initial application. That's normal. It's just after I interview with a company 2 or 3 times for a position and then they ignore my communication that I become quite annoyed.
Example 1: I am currently waiting on a response to a second in-person interview I had with a number of people at company X. I was told that I would "hear back next week" from the hiring manager. 2 weeks later, I sent an email to check in. 1 week later, still no response.
Example 2: A while back with the much more well-known company Y I was told that I would "receive feedback soon" by a recruiter after they had flown me out and had dedicated basically a half-day worth of interviews for me with their team. I followed-up 1 week later and received a message that "the team has been busy" and that they'll "get back to [me] next week." I sent another email checking in 2 weeks later. Ignored. I tried again 2 or 3 weeks later after that. Ignored again. And just because I still had the recruiter's email address, I followed-up 2 months later and finally got an email that the position had actually been removed.