Interpreting polyphonic compositions oftentimes can be quite challenging, introducing a lot of confusion related to the very concept of polyphonic music. The aim of this paper is to indicate challenges and obstacles encountered while performing works of such kind, with the emphasis being put on the works of Johann Sebastian Bach and Ludwig van Beethoven. Highest point of instrumental polyphonic music and its most significant and most developed form is found in fugue, the form which is also most frequently found in piano literature. Apart from Johann Sebastian Bach, who is unsurpassable in mastering baroque fugue and other polyphonic compositions, many other composers of various musical periods have given their contribution in creating polyphonic works, one of the most significant being Ludwig van Beethoven. A part of this paper deals with analysis and comparisson of two polyphonic compositions: Fugue in D minor, BWV 875 and Sonata in F major, op.10, no.2, III Presto. Although these are two different forms of instrumental music, their common characteristics can be found on many levels. Among the first and most significant is the polyphonic texture with its highly complex structure, which requires perfomer's deep knowledge on polyphonic forms. Apart from this, a performer needs to have a high level of technical knowledge required for the proper interpretation of these compositions. Oftentimes pianists who easily perform complex homophonic compositions encounter numerous difficulties in performing polyphonic ones. Therefore, it is highly important to learn how to perform polyphonic techniques from the very beginning of playing piano. Apart from technical difficulties that need to be mastered, it is necessary to have a high level of theoretical knowledge and understanding of polyphonic music and its role in various music styles, with the single purpose of better interpreting such works.