In long-term-evolution-advanced (LTE-advanced), heterogeneous deployments of relays, femtocells and conventional macrocells are expected to provide coverage extension and throughput enhancement, while significantly lowering the energy consumption and total-cost-of-ownership (TCO) in cellular networks. This study presents a methodology for estimating the total energy consumption, taking into account the total operational power and embodied energy, and TCO of wireless cellular networks, and in particular provides a means to compare homogeneous and heterogeneous network (HetNets) deployments. The authors introduce realistic energy models and energy metrics based on information available from mobile-network operators (MNOs) and base stations manufacturers. Additionally, up-to-date operational and capital expenditure (OPEX and CAPEX) models are used to calculate TCO of candidate networks. The authors evaluate two scenarios for HetNets, namely a joint macro-relay network and a joint macro-femtocell network, with different relay and femtocell deployments densities. The results obtained show that compared to macro-centric networks, joint macro-relay networks are both energy and cost efficient, whereas joint macro-femtocell networks reduce the networks TCO at the expense of increased energy-consumption. Finally, it is observed that energy and cost gains are highly sensitive to the OPEX model adopted.