The paper demonstrates the use of phase diagrams as tools for visualizing and exploring meromorphic functions. The representation of a real function by its graph is one of the most insightful tools that mathematics has developed. Besides different types of grid mappings, which reflect conformality, one of the most promising ideas is the use of color. For example, coloring the graph of the modulus of a function \(f\) according to its argument yields the colored analytic landscape of \(f\). Another approach is the so-called domain coloring, which color-codes the values \(f(z)\) of a function \(f\) using a two-dimensional color scheme, and depicts them directly on the domain. Compared with the colored analytic landscape, domain colorings have the advantage that they live in two space dimensions, which makes it easier to represent complicated functions. However, standard domain coloring often results in somewhat fuzzy pictures, so that it is difficult, for example, to locate zeros precisely. Different modifications have been proposed to eliminate this shortcoming. An extreme variant is to omit the modules completely and to display only the color-coded argument. This paper follows one of these lines, which associates with any meromorphic function \(f\) a dynamical system. This system endows the domain of \(f\) with a phase flow and converts the phase plot into a phase diagram. With any meromorphic function \(f : D\to\widehat{\mathbb C}\) on an open connected domain \(D\subset\widehat{\mathbb C}\), two mappings \[ P_f:D\to\mathbb T\cup(0,\infty),\quad z\mapsto\frac{f(z)}{|f(z)|},\qquad \quad V_f:D\to\mathbb C,\quad z\mapsto-\frac{f(z)\overline{f'(z)}}{|f(z)|^2+|f'(z)|^2}, \] are associated with an appropriate definition at the zeros and poles. Color-coding the points of \(\mathbb T\cup\{0,\infty\}\) converts the function \(P_f\) to an image which visualizes the function \(f\) directly on its domain. Endowing this phase plot with the orbits of the vector field \(V_f\) yields the phase diagram of \(f\). The author describes the local normal forms of phase diagrams, studies the properties of their orbits, and investigates the cells and the basins of attraction of zeros with respect to the phase flow. Special attention is paid to the interplay between zeros, poles and saddles of meromorphic functions considering special Jordan domains \(G\) with piecewise isochromatic boundary. In particular, formulas are derived which relate the numbers of critical points in a Jordan domain \(G\) to the winding numbers of \(P_f\) and \(V_f\) along the boundary of \(G\). A short proof of Walsh's theorem on the number of critical points of Blaschke products serves as an illustration. Phase plots facilitate a fresh view on known results and may open new perspectives.