diff --git a/docs/src/models/rpmodel.rst b/docs/src/models/rpmodel.rst
index 47eba01262..91ef71872a 100644
--- a/docs/src/models/rpmodel.rst
+++ b/docs/src/models/rpmodel.rst
@@ -5,4 +5,6 @@
     :synopsis: Random Projections
     :members:
     :inherited-members:
-
+    :undoc-members:
+    :show-inheritance:
+    :special-members: __getitem__
diff --git a/gensim/models/rpmodel.py b/gensim/models/rpmodel.py
index 0c8f7c8b26..0826a7c359 100644
--- a/gensim/models/rpmodel.py
+++ b/gensim/models/rpmodel.py
@@ -5,6 +5,35 @@
 # Licensed under the GNU LGPL v2.1 - http://www.gnu.org/licenses/lgpl.html
 
 
+"""Random Projections (also known as Random Indexing).
+
+For theoretical background on Random Projections, see [1]_.
+
+
+Examples
+--------
+>>> from gensim.models import RpModel
+>>> from gensim.corpora import Dictionary
+>>> from gensim.test.utils import common_texts, temporary_file
+>>>
+>>> dictionary = Dictionary(common_texts)  # fit dictionary
+>>> corpus = [dictionary.doc2bow(text) for text in common_texts]  # convert texts to BoW format
+>>>
+>>> model = RpModel(corpus, id2word=dictionary)  # fit model
+>>> result = model[corpus[3]]  # apply model to document, result is vector in BoW format
+>>>
+>>> with temporary_file("model_file") as fname:
+...     model.save(fname)  # save model to file
+...     loaded_model = RpModel.load(fname)  # load model
+
+
+References
+----------
+.. [1] Kanerva et al., 2000, Random indexing of text samples for Latent Semantic Analysis,
+       https://cloudfront.escholarship.org/dist/prd/content/qt5644k0w6/qt5644k0w6.pdf
+
+"""
+
 import logging
 
 import numpy as np
@@ -16,30 +45,21 @@
 
 
 class RpModel(interfaces.TransformationABC):
-    """
-    Objects of this class allow building and maintaining a model for Random Projections
-    (also known as Random Indexing). For theoretical background on RP, see:
-
-      Kanerva et al.: "Random indexing of text samples for Latent Semantic Analysis."
 
-    The main methods are:
+    def __init__(self, corpus, id2word=None, num_topics=300):
+        """
 
-    1. constructor, which creates the random projection matrix
-    2. the [] method, which transforms a simple count representation into the TfIdf
-       space.
+        Parameters
+        ----------
+        corpus : iterable of iterable of (int, int)
+            Input corpus.
 
-    >>> rp = RpModel(corpus)
-    >>> print(rp[some_doc])
-    >>> rp.save('/tmp/foo.rp_model')
+        id2word : {dict of (int, str), :class:`~gensim.corpora.dictionary.Dictionary`}, optional
+            Mapping `token_id` -> `token`, will be determine from corpus if `id2word == None`.
 
-    Model persistency is achieved via its load/save methods.
-    """
+        num_topics : int, optional
+            Number of topics.
 
-    def __init__(self, corpus, id2word=None, num_topics=300):
-        """
-        `id2word` is a mapping from word ids (integers) to words (strings). It is
-        used to determine the vocabulary size, as well as for debugging and topic
-        printing. If not set, it will be determined from the corpus.
         """
         self.id2word = id2word
         self.num_topics = num_topics
@@ -50,8 +70,13 @@ def __str__(self):
         return "RpModel(num_terms=%s, num_topics=%s)" % (self.num_terms, self.num_topics)
 
     def initialize(self, corpus):
-        """
-        Initialize the random projection matrix.
+        """Initialize the random projection matrix.
+
+        Parameters
+        ----------
+        corpus : iterable of iterable of (int, int)
+          Input corpus.
+
         """
         if self.id2word is None:
             logger.info("no word id mapping provided; initializing from corpus, assuming identity")
@@ -73,8 +98,32 @@ def initialize(self, corpus):
         # are smarter and this is no longer needed?
 
     def __getitem__(self, bow):
-        """
-        Return RP representation of the input vector and/or corpus.
+        """Get random-projection representation of the input vector or corpus.
+
+        Parameters
+        ----------
+        bow : {list of (int, int), iterable of list of (int, int)}
+            Input document or corpus.
+
+        Returns
+        -------
+        list of (int, float)
+            if `bow` is document OR
+        :class:`~gensim.interfaces.TransformedCorpus`
+            if `bow` is corpus.
+
+        Examples
+        ----------
+        >>> from gensim.models import RpModel
+        >>> from gensim.corpora import Dictionary
+        >>> from gensim.test.utils import common_texts
+        >>>
+        >>> dictionary = Dictionary(common_texts)  # fit dictionary
+        >>> corpus = [dictionary.doc2bow(text) for text in common_texts]  # convert texts to BoW format
+        >>>
+        >>> model = RpModel(corpus, id2word=dictionary)  # fit model
+        >>> result = model[corpus[0]]  # apply model to document, result is vector in BoW format, i.e. [(1, 0.3), ... ]
+
         """
         # if the input vector is in fact a corpus, return a transformed corpus as result
         is_corpus, bow = utils.is_corpus(bow)
@@ -96,5 +145,13 @@ def __getitem__(self, bow):
         ]
 
     def __setstate__(self, state):
+        """Sets the internal state and updates freshly_loaded to True, called when unpicked.
+
+        Parameters
+        ----------
+        state : dict
+           State of the class.
+
+        """
         self.__dict__ = state
         self.freshly_loaded = True