This paper presents some recent ideas on and methods created by power engineers for the solution of the Load Flow Problem. Beginning with an analysis of the solution of large systems of linear equations, techniques employing elementary matrix operations are discussed to reduce the amount of calculations necessary to achieve repeated solutions. Recent interest in taking advantage of the characteristic sparsity of the admittance matrix is also examined. The problems of operating on and computer storage of large sparse matrices are investigated. Methods to efficiently order, store and work with large sparse matrices are discussed and demonstrated. The general acceptance and use of Newton's Method by power engineers for Load Flow Studies has resulted in many variations on it. Together with a review of the Load Flow Problem and Newton's Method, an analysis of three related methods is presented and a comparison of their characteristics is made to Newton's Method. This paper serves to keep the power engineer abreast of the many recent advances available for conducting Load Flow Studies.