Recently, neural models have been proposed for headline generation by leing to map documents to headlines with recurrent neural network. In this work, we give a detailed introduction and comparison of existing work and recent improvements in neural headline generation, with particular attention on how encoders, decoders and neural model training strategies alter the overall performance of the headline generation system. Furthermore, we perform quantitative analysis of most existing neural headline generation systems and summarize several key factors that impact the performance of headline generation systems. Meanwhile, we carry on detailed error analysis to typical neural headline generation systems in order to gain more comprehension. Our results and conclusions are hoped to benefit future research studies.