This work, presents an extensive literature review that highlights innovation opportunities and presents novel solutions for the main uplink mMTC problems. Based on the adaptive Recursive Least Squares (RLS) algorithm, the proposed regularized techniques jointly performs activity detection and signal decoding, without the need to perform explicit channel estimation. In order to improve the detection performance, a list detection technique that uses two candidate-list schemes is developed. Rewriting the problem with factor-graphs, novel message-passing algorithms with dynamic scheduling that jointly estimates the channels and detects devices activity are proposed. Lastly, a complete message-passing solution is presented, where LDPC decoding beliefs are introduced in the system, in a way that the algorithm besides the channel estimation and activity detection, also jointly decodes the signals. In order to evaluate the proposed techniques, numerical results are provided as well as a computational complexity, state-evolution, convergence and a diversity analysis. Uplink sum-rate expressions that take into account metadata collisions, interference and a variable activity probability for each user are also derived. Finally, conclusions and future directions are discussed.