  In this paper, we present an overview of different types of random walk
strategies with local and non-local transitions on undirected connected
networks. We present a general approach to analyzing these strategies by
defining the dynamics as a discrete time Markovian process with probabilities
of transition expressed in terms of a symmetric matrix of weights. In the first
part, we describe the matrices of weights that define local random walk
strategies like the normal random walk, biased random walks, random walks in
the context of digital image processing and maximum entropy random walks. In
addition, we explore non-local random walks like L\'evy flights on networks,
fractional transport and applications in the context of human mobility.
Explicit relations for the stationary probability distribution, the mean first
passage time and global times to characterize the random walk strategies are
obtained in terms of the elements of the matrix of weights and its respective
eigenvalues and eigenvectors. Finally, we apply the results to the analysis of
particular local and non-local random walk strategies; we discuss their
efficiency and capacity to explore different types of structures. Our results
allow to study and compare on the same basis the global dynamics of different
types of random walk strategies.
