Deep learning (DL) becomes increasingly pervasive, being used in a wide range of software applications. These software applications, named as DL based software (in short as DL software), integrate DL models trained using a large data corpus with DL programs written based on DL frameworks such as TensorFlow and Keras. A DL program encodes the network structure of a desirable DL model and the process by which the model is trained using the training data. To help developers of DL software meet the new challenges posed by DL, enormous research efforts in software engineering have been devoted. Existing studies focus on the development of DL software and extensively analyze faults in DL programs. However, the deployment of DL software has not been comprehensively studied. To fill this knowledge gap, this paper presents a comprehensive study on understanding challenges in deploying DL software. We mine and analyze 3,023 relevant posts from Stack Overflow, a popular Q&A website for developers, and show the increasing popularity and high difficulty of DL software deployment among developers. We build a taxonomy of specific challenges encountered by developers in the process of DL software deployment through manual inspection of 769 sampled posts and report a series of actionable implications for researchers, developers, and DL framework vendors.