During the past decade, increasing use has been made of fractals to model natural phenomena and objects. The most widely used parameter is the fractal dimension; strictly speaking, a non-integer number between 1.0 and 2.0 for a linear object such as a coastline, and 2.0 and 3.0 for the surface of a solid object. A large number of algorithms have been developed for estimating fractal dimension, and it is not uncommon that these algorithms yield significantly different results when applied to the same data set. It is therefore of considerable importance to understand the true nature of the object being modeled, and to use the most appropriate algorithm for the particular application. A number of algorithms have been examined for use in various applications such as environmental sciences, planetary observations, geology, meteorology, and medical diagnosis and research. Specific problems with using fractal analysis in these applications are addressed.