This paper presents a tractable and accurate model for downlink heterogeneous cellular networks (HCNs) consisting of K tiers of randomly located base stations (BSs), each with different average transmit power, data rate, and BS density. The model assumes a mobile user connects to the strongest BS, and derives an expression for coverage probability (equivalently outage probability) under both open and closed access scenarios. The derived expression has a simple closed-form in the high SINR regime and is accurate down to -4 dB. The model is validated against an actual LTE network and is shown to be accurate within 1-2 dB. The paper also derives the average rate achieved by a randomly located mobile and the average load on each tier of BSs. Key findings include that in interference-limited open access networks, adding more tiers or BSs does not affect coverage probability when all tiers have the same target SINR. The model is applicable to both non-orthogonal and orthogonal cellular networks and can be extended to include various enhancements like opportunistic scheduling and multiple antenna communication. The paper also discusses the applicability of the model to different deployment scenarios and highlights the importance of considering non-homogeneous user distributions and realistic traffic models for optimal cell association policies in heterogeneous networks.This paper presents a tractable and accurate model for downlink heterogeneous cellular networks (HCNs) consisting of K tiers of randomly located base stations (BSs), each with different average transmit power, data rate, and BS density. The model assumes a mobile user connects to the strongest BS, and derives an expression for coverage probability (equivalently outage probability) under both open and closed access scenarios. The derived expression has a simple closed-form in the high SINR regime and is accurate down to -4 dB. The model is validated against an actual LTE network and is shown to be accurate within 1-2 dB. The paper also derives the average rate achieved by a randomly located mobile and the average load on each tier of BSs. Key findings include that in interference-limited open access networks, adding more tiers or BSs does not affect coverage probability when all tiers have the same target SINR. The model is applicable to both non-orthogonal and orthogonal cellular networks and can be extended to include various enhancements like opportunistic scheduling and multiple antenna communication. The paper also discusses the applicability of the model to different deployment scenarios and highlights the importance of considering non-homogeneous user distributions and realistic traffic models for optimal cell association policies in heterogeneous networks.