Measurements of atomic parity violation provide important cross-tests of the standard model of electroweak interactions by probing these interactions in the domain of low energies. The effects of parity nonconservation in atoms, both dependent and not dependent on nuclear spin, have been successfully measured in experiments. The existence of permanent electric dipole moment (EDM) of a quantum particle requires that fundamental parity (P) and time-reversal (T) symmetries are violated. By the CPT theorem, this would mean violation of the combined CP (charge conjugation-parity) symmetry as well. Studies of T and CP violation in nature provide valuable information for theories of baryogenesis, and for understanding of fundamental interactions in general. Recently, a new wave of experiments has been initiated to measure the effects of P and T violation in solid state materials. The possibility to substantially increase the experimental sensitivity lies in the larger number of particles compared to the atomic experiments and in the specific collective effects in solids. The downside is the typically larger level of systematics. In the present work, the following effects due to violation of T and P at fundamental level in solids are considered: (a) effects due to the nuclear weak charge (violation of P) in rare-earth trifluorides, a possibility exists to measure the Weinberg angle with high precision; (b) effects due to the nuclear anapole moment (nuclear spin-dependent violation of P) in praseodymium and thulium garnets, the NMR-type experiments can possibly be used to measure nuclear anapole moments of Pr and Tm; (c) effects due to the electron EDM in gadolinium garnets, increase of the experimental sensitivity to the electron EDM of several orders of magnitude is possible; (d) effects due to the nuclear Schiff moment of 207Pb in ferroelectric lead-titanate; this possibility looks particularly promising, offering a potential 10 orders of magnitude increase of sensitivity to the nuclear Schiff moment, which puts the standard model prediction for this value within experimental reach. Also discussed are several other possibilities for experimental observation of these effects and the impact of some possible systematic effects on the proposed measurements.