What are the current killing machine learning methods?
The question is very general. However, there are some studies being conducted to test which algorithms perform relatively well in a broad range of problems (I'll add link to papers later), concerning regression and classification.

Lately Random Decision Forests, Support Vector Machines and certain variations of Neural Networks are being said to achieve the best results for very broad variety of problems.

This does not mean that these are "the best algorithms" for any problem, that does not exist, and actually is not very realistic to pursue. Also it must be observed that both RDF and SVM are rather-easy methods to initially grasp and obtain good results, so they are becoming really popular. NN have been used intensively since couple of decades (after they revived), so they appear often in implementations.

If you are interested in learning further you should look for an specific area and deal with a problem that can be solved nicely by machine learning to understand the main idea (and why is impossible to find  the method).

You will find common the task to try to predict the expected behavior of something given some known or observable characteristics (to learn the function that models the problem given input data), the issues related to dealing with data in high-dimensional spaces, the need for good quality data, the notable improvements that can give data pre-processing, and many others.