Photonic band gap structures have a high potential for nearly zero-threshold lasers. This paper describes new-types of low-threshold photonic crystal lasers fabricated in InGaAsP slab waveguides free-standing in air. Two-types of photonic crystal lasers are studied. One is a single-cell nano-cavity laser formed in a square array of air holes. This photonic band gap laser operates in the smallest possible whispering gallery mode with a theoretical Q >30000 and exhibits low threshold pump power of 0.8 mW at room temperature. The nther laser does not have any cavity structure and the lasing operation originates from the enhanced optical density of states near photonic band edges. A very low threshold of 35 $mu$W (incident pump power) is achieved from this laser at 80 K, one of the lowest values ever reported. This low threshold is benefited from low optical losses as well as enhanced material gain at low temperature.