There is an intense debate regarding the best way to attract investment for the long-term expansion of an electricity transmission network. We study three hypotheses: the long-term financialtransmission- right hypothesis; the incentive-regulation hypothesis; and the market-power hypothesis. The first approach derives optimal transmission expansion through auctions of longterm financial transmission rights by an independent system operator. The second provides a Transco with incentives to expand the network by making it face the entire social cost of congestion. The third approach defines optimal transmission expansion according to the strategic behavior of generators. This paper discusses the analytical and practical strengths and weaknesses of each approach.