"Although fractal geometry is a relatively recent area of mathematical research, with almost all major results being within the last century, it has quickly become popular for its vast number of applications to other areas of math, as well as its interesting sets which can arise when studying the subject. We give a (very brief) introduction to the study of fractals, the key definitions, and important theorems. Although fractal geometry requires a high level of math to enter, it's underlying ideas are quite intuitive, and we present those in a way which should be accessible to everyone. We also discuss various current research topics, with an emphasis those topics which are happening at U.N.T. The goal being, of course, to encourage any first-year graduate students who may be interested in the field."