  In this paper, we survey and study definitions and properties of tropical
polynomials, tropical rational functions and in general, tropical meromorphic
functions, emphasizing practical techniques that can really carry out
computations. For instance, we introduce maximally represented tropical
polynomials and tropical polynomials in compact forms to quickly find roots of
given tropical polynomials. We also prove the existence and uniqueness of
tropical theorems for meromorphic functions with prescribed roots and poles.
Moreover, we explain the relations between classical and tropical meromorphic
functions. Different definitions and applications of tropical meromorphic
functions are discussed. Finally, we point out the properties of tropical
meromorphic functions are very similar to complex ones and prove some tropical
analogues of theorems in complex analysis.
