Causal Inference
The fundamental problem of causal inference is that we can not see both what happened and what would have happened. This leads to two types of people: the correlation is causation, and the correlation does not imply causation, therefore we're done. Causal inference researchers try to straddle the middle ground.
Machine Learning
Machine Learning is probably one of the hottest, misused, and misleading terms in statistics. It basically boils down to fancy regression, and has many of the same issues as classic regression (overfitting, garbage in-garbage out, computation time), albeit while allowing for greater predictive capabilities and relaxed assumptions.
Miscellaneous
Statistics are widely used in many fields, including physics, astronomy, sociology, marketing, economics, sports, biology, logistics, and more.
The best thing about being a statistician is that you get to play in everyone's backyard -John Tukey