What is the problem when a car goes into reverse and won't go into drive?

If you can't physically shift the vehicle into drive, then the linkage going to the transmission may be binding up. If you can shift the gear selector into drive, but the vehicle won't move forward, then you may be very low on fluid. Many times when a transmission gets very low, it will only move in reverse and not forward in any gear. Check the fluid level and top it off if it is low. If the transmission is already full, then you may have more serious damage that may require a trans shop.