Abstract: In the last two decades, the critical properties of colossal magnetoresistive perovskite manganites and multiferroic hexagonal manganites have been explored to a great extent. In the case of perovskite manganites, for varying chemical compositions a widely varying critical exponents including tricritical mean-field have been obtained near their paramagnetic-to-ferromagnetic (PM-FM) phase transitions. In order to capture such varying universality classes, we take into account in the model Hamiltonian the experimentally observed fact that spin-lattice interaction in such systems plays an important role in determining their critical behavior. In the $\phi^4$-model such spin-lattice interaction generates a nonlocal quartic term in the effective model Hamiltonian. Considering a nonlocal $\phi^4$-model Hamiltonian, we determine its underlying universality classes and show that it captures well the widely varying experimental results for varying values of nonlocal exponent at one-loop order of our renormalization-group calculations. Spin-lattice interactions are also found to play a prominent role in hexagonal antiferromagnetic manganites. To determine their critical behavior near paramagnetic-to-antiferromagnetic (PM-AFM) phase transitions, we proceed with a nonlocal model $C$ Hamiltonian and investigate its critical properties. Our results are found to be in well agreement with the available experimental estimate.