Great questions. I'm going to answer them in two posts because I'm rather busy this week.
I have experience with this from both sides, so this might be helpful. And from both sides, the short answer is that it's all about the quality of your resume. That's the source document that should always be the focus. How ones gets to your resume varies of course based on the platform(s) used and the sophistication of the company and you.
From the job seeker perspective, the answer is follow up. You can do this is several ways, but what gets my attention is someone showing me that they actually have interest in the company. One can do that by keeping an eye on the companies that view your profile. Review them, go to their sites and look at their job posting to see what they are probably looking at you for; and if you're interested, contact them. Ask to speak, or the email for; the Hiring Manager for that position. I can guarantee that will get their attention. Because companies have the opposite perspective. One that says, "These people are just spamming out their resumes and don't care about this company, it's culture, values, history, or products." And that represents 95% of all candidates. So showing you actually want to work for that specific company will land you in the remaining 5%.
From the employer perspective, it's initially 100% about your resume. Meaning, is this person a good fit. And, sadly, most resumes are qualifying and not quantifying when it comes to details about experiences. So only part of the picture of your experiences are provided for evaluation. And as it turns out, blocks of text about someone explaining in exaggerated terms how great they are is rather boring. So provide numbers. It breaks out the text, it stands out, and will be a major part of the focus for the reviewer. For example, "I've been building widgets for 10 years." Okay, great. How big are they, how many have you produced, what was the sell price for the biggest or most complex widget that you've ever produced, etc.
Sadly, however, more sophisticated companies use algorithms for key-word searches. So make sure you have the key words from the position description of the job(s) you want in your resume. This is precisely why a one-size-fits-all resume is a losing resume. Tailor them. Find the job you really want, and are qualified for, and focus on that position. If it doesn't work out, find the next one.
Bottom line: It takes focus and effort. A passive approach is a losing approach. Unless of course, your famous in your area of expertise. However, in that case, you wouldn't need to reach out to anyone.
Hope that helps.