Phase transitions in several quenched random systems are studied. We used the Migdal-Kadanoff renormalization group method and Monte Carlo simulations. The critical behavior of the quenched random systems exhibits a drastic change from that of the corresponding pure systems. We first studied the critical behavior of the directed polymer on the disordered hierarchical lattice. Using a Monte Carlo method, we obtained the fixed distribution of the random energy from which we calculated the critical exponent and the specific heat. We also studied random field Ising model on the hierarchical lattice. It is found that magnetization exponent is nonvanishing though small due to the fact that the fixed distribution of the couplings has a finite weight at zero. We also show this result analytically. Finally, we studied phase transitions in a fractal porous media. Our fractal model can be described as a two parameter Mandelbrot percolation process which generates a solid fractal with pores on all length scales. We study the connectivity of the pores and the solid as well. It is found that there is a critical dimension $D\sb{c}.$ If D $>$ $D\sb{c},$ there is no percolation phase transition, while for D $<$ $D\sb{c},$ there is a percolation transition and the correlation length exponent $\nu$ is D dependent. Furthermore, we studied thermal phase transitions of spin systems with spins placed in the pore space. In the thermodynamic limit, the specific heat is the same as that of the pure system. The renormalized couplings, however, exhibit two fixed distributions with one at the bulk phase transition $T\sb{c0}$ and the other at a temperature $T\sb{c}$ lower than $T\sb{c0}.$ The correlation length exponent at $T\sb{c}$ is considerably larger than that of the bulk phase transition. If the system is finite, our simulation shows that the specific heat has two peaks at $T\sb{c0}$ and $T\sb{c}.$