By far the most comprehensive digital research tool that I use is Google Analytics. The functions of this tool are many, but I will cover some of the ones that are important for my work. At the front page you see your very basic information such as visits, pageview, bounce rate etc..
Visits can be looked at over a period of time to determine how well you SEO or SEM campaign is doing to get visitors to your homepage. Ideally you would like to see a spike in the data when a SEM campaign is going on. To determine that it is in fact a SEM campaign you can view sources of traffic. This will split the data into search traffic, referral traffic, direct traffic and campaigns.
A visitor flow chart can function like the heat charts that we saw in class. You can view Where visitors start and what pages they travel to next. From the homepage of twincityinvisalign.com, a website I manage, the most common next page is the promotion page. So I can tell from looking at the flow chart that the advertisement that I have on the homepage which links to the promotion page is functioning well.
A relatively new feature to Google analytics is called experiment. I haven't tried this feature out yet but it ultimately is a tool to improve conversions on your website by testing 2 or more different versions of the landing page to see which one performs the best. There is significantly more information on Google Analytics but these are some of the functions I use and find cool!