After a brief overview about torsion in homology and examples of complexes with small torsion and few vertices we will 
focus our attention on a particular series of examples. In particular, we will construct a series HMT(n) of 2-dimensional simplicial complexes with huge torsion, |H_1(HMT(n))|=|det(H(n))|=n^(n/2), where the construction is based on the Hadamard matrices H(n) and they have linearly many vertices in n. Our explicit series improves a previous construction by Speyer, narrowing the gap to the highest possible asymptotic torsion growth achieved by Newman via a randomized construction.