Recently, iterative receiver combining multiple-input multiple-output (MIMO) detection with channel decoding has been widely considered to achieve near-capacity performance and reliable high data rate transmission, for future wireless communication systems. However, such iterative processing increases the computational complexity at the receiver. In this paper, the computational complexity of MIMO detection algorithms combined with turbo decoding is investigated. We first present an overview of the family of MIMO detection algorithms based on sphere decoding, K-Best decoding, and interference cancellation. A recently proposed low-complexity K-Best decoder (LC-K-Best) is also presented. Moreover, we analyze the convergence of combining these detection algorithms with the turbo decoder using the extrinsic information transfer (EXIT) chart. Consequently, a new scheduling order of the number of iterations for the iterative process is proposed. Several system configurations are developed and compared in terms of performance and complexity. Simulations and analytical results show that the new scheduling provides good performance with a large saving in the complexity. Additionally, the LC-K-Best decoder shows a good performance-complexity tradeoff, and it is therefore suitable for parallel and pipeline architectures that can meet high throughput requirements.