Multiple soliton solutions are fundamental excitations. There are many kinds of equivalent representations for multiple soliton solutions such as the Hirota forms, Wronskian and/or double Wronskian expressions and Phaffian representations. Recently, in the studies of multi-place nonlocal systems, we find that there are a type of novel but equivalent simple and elegant forms to describe multiple soliton solutions for various integrable systems. In this paper, we mainly review novel types of expressions of multiple soliton solutions for some kinds of nonlinear integrable systems. Meanwhile, some completely new expressions for the Sawada-Kortera equations, the asymmetric Nizhnik-Novikov-Veselov system, the modified KdV equation, the sine-Gordon equation, the Ablowitz-Kaup-Newell-Segue system and the completely discrete H₁ equation are firstly given in this paper. New expressions usually possess explicit full reversal symmetries including parity, time reversal, soliton initial position reversal and charge conjugate reversal. These kinds of explicitly symmetric forms are very useful and convenient in the studies on the nonlinear physical problems such as the multi-place nonlocal systems and the resonant structures.