The "era of phase transitions" began with the discovery of the heat capacity and latent heat in the eighteenth century. A half century after that, critical phenomena emerged and had its heyday with the critical opalescence seen in carbon dioxide. It took, however, another 100 years to obtain an explanation of the microscopic ingredients underlying these intriguing phenomena. This achievement lead to Wilson's noble prize. Possible generalizations, sometimes not so easily reproduced in experiments, could be foreseen from theoretical grounds, leading to the discovery of multicritical behavior. We will present some models defined on regular lattices, mainly magnetic spin systems and geometrical polymers, which exhibit a variety of multicritical phenomena that can be studied via computer simulations as well as theoretical approaches.