diff --git a/bask/acquisition.py b/bask/acquisition.py
index d993acc..5e47928 100644
--- a/bask/acquisition.py
+++ b/bask/acquisition.py
@@ -132,6 +132,16 @@ def _ei_f(x):
 
 
 class ExpectedImprovement(UncertaintyAcquisition):
+    """Select the point maximizing the expected improvement over the current
+    optimum.
+
+    Parameters
+    ----------
+    y_opt : float, default=None
+        The value of the current optimum. If it is None, it will use the
+        minimum y value of the evaluated points.
+    """
+
     def __call__(self, mu, std, *args, y_opt=None, **kwargs):
         if y_opt is None:
             y_opt = mu.min()
@@ -143,6 +153,16 @@ def __call__(self, mu, std, *args, y_opt=None, **kwargs):
 
 
 class TopTwoEI(ExpectedImprovement):
+    """Select the point with the highest expected improvement over the
+    point with the maximum expected improvement overall.
+
+    Parameters
+    ----------
+    y_opt : float, default=None
+        The value of the current optimum. If it is None, it will use the
+        minimum y value of the evaluated points.
+    """
+
     def __call__(self, mu, std, *args, y_opt=None, **kwargs):
         ei = super().__call__(mu, std, *args, y_opt=y_opt, **kwargs)
         values = np.zeros_like(mu)
@@ -155,18 +175,42 @@ def __call__(self, mu, std, *args, y_opt=None, **kwargs):
 
 
 class Expectation(UncertaintyAcquisition):
+    """Select the point with the lowest estimated mean."""
+
     def __call__(self, mu, std, *args, **kwargs):
         return -mu
 
 
 class LCB(UncertaintyAcquisition):
-    def __call__(self, mu, std, *args, alpha=1.86, **kwargs):
+    """Select the point with the lowest lower confidence bound.
+
+    Parameters
+    ----------
+    alpha : positive float, alpha=1.96
+        Number of standard errors to substract from the mean estimate.
+    """
+
+    def __call__(self, mu, std, *args, alpha=1.96, **kwargs):
         if alpha == "inf":
             return std
         return alpha * std - mu
 
 
 class MaxValueSearch(UncertaintyAcquisition):
+    """Select points based on their mutual information with the optimum value.
+
+    Parameters
+    ----------
+    n_min_samples : int, default=1000
+        Number of samples for the optimum distribution
+
+    References
+    ----------
+    [1] Wang, Z. & Jegelka, S.. (2017). Max-value Entropy Search for Efficient
+        Bayesian Optimization. Proceedings of the 34th International Conference
+        on Machine Learning, in PMLR 70:3627-3635
+    """
+
     def __call__(self, mu, std, *args, n_min_samples=1000, **kwargs):
         def probf(x):
             return np.exp(np.sum(st.norm.logcdf(-(x - mu) / std), axis=0))
@@ -201,12 +245,19 @@ def probf(x):
 
 
 class ThompsonSampling(SampleAcquisition):
+    """Sample a random function from the GP and select its optimum."""
+
     def __call__(self, gp_sample, *args, **kwargs):
         return -gp_sample
 
 
 class VarianceReduction(FullGPAcquisition):
-    """ A criterion which tries to find the region where it can reduce the variance the most."""
+    """A criterion which tries to find the region where it can reduce the
+    global variance the most.
+
+    This criterion is suitable for active learning, where the goal is to
+    uniformly estimate the target function and not only its optimum.
+    """
 
     def __call__(self, X, gp, *args, **kwargs):
         n = len(X)
@@ -227,13 +278,14 @@ def __call__(self, X, gp, *args, **kwargs):
 class PVRS(FullGPAcquisition):
     """Implements the predictive variance reduction search algorithm.
 
-    The algorithm draws a set of Thompson samples (samples from the optimum distribution) and proposes the point which
-    reduces the predictive variance of these samples the most.
+    The algorithm draws a set of Thompson samples (samples from the optimum
+    distribution) and proposes the point which reduces the predictive variance
+    of these samples the most.
 
     References
     ----------
-    [1] Nguyen, Vu, et al. "Predictive variance reduction search." Workshop on Bayesian optimization at neural
-        information processing systems (NIPSW). 2017.
+    [1] Nguyen, Vu, et al. "Predictive variance reduction search." Workshop on
+    Bayesian optimization at neural information processing systems (NIPSW). 2017.
     """
 
     def __call__(self, X, gp, *args, n_thompson=10, random_state=None, **kwargs):