  Given a sequence $X=(X_1,X_2,\ldots)$ of random observations, a Bayesian
forecaster aims to predict $X_{n+1}$ based on $(X_1,\ldots,X_n)$ for each $n\ge
0$. To this end, in principle, she only needs to select a collection
$\sigma=(\sigma_0,\sigma_1,\ldots)$, called ``strategy" in what follows, where
$\sigma_0(\cdot)=P(X_1\in\cdot)$ is the marginal distribution of $X_1$ and
$\sigma_n(\cdot)=P(X_{n+1}\in\cdot\mid X_1,\ldots,X_n)$ the $n$-th predictive
distribution. Because of the Ionescu-Tulcea theorem, $\sigma$ can be assigned
directly, without passing through the usual prior/posterior scheme. One main
advantage is that no prior probability is to be selected. In a nutshell, this
is the predictive approach to Bayesian learning. A concise review of the latter
is provided in this paper. We try to put such an approach in the right
framework, to make clear a few misunderstandings, and to provide a unifying
view. Some recent results are discussed as well. In addition, some new
strategies are introduced and the corresponding distribution of the data
sequence $X$ is determined. The strategies concern generalized P\'olya urns,
random change points, covariates and stationary sequences.
