The inadequacies of the national courts in Nigeria which include: the adversarial nature of litigation, unnecessary delays, lack of confidentiality etc has led disputing parties to seek alternative means of dispute resolution, one of which is domestic arbitration. Unfortunately, the potential advantages claimed for arbitration over litigation, are often not achieved in practice. Consequently, the primary focus of the work is the identification and examination of some problems and challenges hindering the law, practice, institution and growth of domestic commercial arbitration and customary arbitration in Nigeria. In the work, relevant suggestions are made for tackling these problems and challenges. The modest contribution of the work to the field of arbitration should help shed some light on this emerging and exciting field of dispute resolution in Nigeria, and should be especially useful to scholars, lawyers and other professionals in arbitration.