There are several ways we can run hills and they all serve their own purposes, many times one feeding off of the other.
Hill repeats: The ultimate hill workout and, according to many coaches and athletes including people like Lydiard and Eyestone, the ultimate strength training workout for distance runners. This is the most demanding hill workout but also most effective way to build strength you will find useful, whether racing on hills or on the flat. This is where your strength basis comes from.
Hill fartleks: These can be just as intense and effective as hill repeats or much less intense and effective, depending on your course and how you run the fartlek. This can be a good way to build or maintain your strength and, for those who don’t like hill repeats, can be less monotonous while getting in the same type of workout if you can find the right route.
Hilly routes: This is a great workout for initial strength building before hill repeats, a secondary strength workout while doing hill repeats, or maintaining strength after hill repeat phase is over. Simply getting up and down the hills on a course with a number of challenging hills, no matter how hard you push them, will do a lot to build and maintain your strength.
Daily runs on hills: This is another maintenance workout or, for the runner who has done no running on hills yet, a way to introduce the runner to hills. It will not be as effective for strengthening as the above types of runs but you can hit a good hill or two every day without sacrificing your workouts and this will help maintain strength or gradually build into hill running for those who haven’t run on hills before.
Also, it’s important to remember that hills are great for working on your form. I mentioned strengthening here but you could replace strength with form and strengthening with form work throughout this post and it would still hold true.