diff --git a/.travis.yml b/.travis.yml
index 83f0206ed5..bf55dc51d2 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -117,6 +117,12 @@ jobs:
 
     # "test" stage
     ###########################################################################
+    # GNU/Linux, Python 3.8
+    - stage: test
+      name: Python 3.8 Tests Linux
+      <<: *stage_linux
+      python: 3.8
+
     # GNU/Linux, Python 3.7
     - stage: test
       name: Python 3.7 Tests Linux
@@ -137,6 +143,13 @@ jobs:
       <<: *stage_linux
       python: 3.5
 
+    - stage: test
+      name: Python 3.8 Tests OSX
+      <<: *stage_osx
+      python: 3.8
+      env:
+        - PYTHON_VERSION=3.8.0
+
     # OSX, Python 3.7.2 (via pyenv)
     - stage: test
       name: Python 3.7 Tests OSX
diff --git a/CHANGELOG.md b/CHANGELOG.md
index a1e92359d9..291931db46 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -74,6 +74,14 @@ Removed
 Fixed
 -----
 
+Deprecated
+----------
+
+- Python 3.5 support in qiskit-aer is deprecated. Support will be
+  removed on the upstream python community's end of life date for the version,
+  which is 09/13/2020.
+
+
 
 [0.3.2](https://github.com/Qiskit/qiskit-aer/compare/0.3.1...0.3.2) - 2019-10-16
 ===============================================================================
diff --git a/azure-pipelines.yml b/azure-pipelines.yml
index d2385bbff3..b69805bce7 100644
--- a/azure-pipelines.yml
+++ b/azure-pipelines.yml
@@ -45,35 +45,53 @@ jobs:
           python.version: '3.6'
         Python37:
           python.version: '3.7'
+        Python38:
+          python.version: '3.8'
     steps:
       - powershell: Write-Host "##vso[task.prependpath]$env:CONDA\Scripts"
         displayName: Add conda to PATH
       - script: conda create --yes --quiet --name qiskit-aer-$(Build.BuildNumber) python=%PYTHON_VERSION%
         displayName: Create Anaconda environment
-      - script: |
-          call activate qiskit-aer-$(Build.BuildNumber)
-          conda install --yes --quiet --name qiskit-aer-$(Build.BuildNumber) python=%PYTHON_VERSION% numpy
+      - bash: |
+          set -x
+          set -e
+          source activate qiskit-aer-$(Build.BuildNumber)
+          conda install --yes --quiet --name qiskit-aer-$(Build.BuildNumber) python==$(python.version) numpy pip virtualenv
+          conda install -c conda-forge --yes --quiet --name qiskit-aer-$(Build.BuildNumber) python==$(python.version) setuptools
         displayName: Install Anaconda packages
         condition: ne(variables['python.version'], '3.5')
-      - script: |
-          call activate qiskit-aer-$(Build.BuildNumber)
-          conda install --yes --quiet --name qiskit-aer-$(Build.BuildNumber) python=%PYTHON_VERSION% mkl
-          conda install -c conda-forge --yes --quiet --name qiskit-aer-$(Build.BuildNumber) python=%PYTHON_VERSION% openblas
+      - bash: |
+          set -x
+          set -e
+          source activate qiskit-aer-$(Build.BuildNumber)
+          conda install --yes --quiet --name qiskit-aer-$(Build.BuildNumber) python=$(python.version) mkl
+          conda install -c conda-forge --yes --quiet --name qiskit-aer-$(Build.BuildNumber) python=$(python.version) openblas
         displayName: Install Anaconda packages
-        condition: eq(variables['python.version'], '3.5')
+        condition: or(eq(variables['python.version'], '3.5'), eq(variables['python.version'], '3.8'))
       - bash: |
           set -e
           source activate qiskit-aer-$(Build.BuildNumber)
-          git clean -fdX
-          python -m pip install -U pip virtualenv setuptools
-          pip install cython
+          conda install -c conda-forge --yes --quiet --name qiskit-aer-$(Build.BuildNumber) python=$(python.version) osqp
+          pip install -r requirements-dev.txt
           pip install git+https://github.com/Qiskit/qiskit-terra.git
-          pip install --ignore-installed -r requirements-dev.txt
+        displayName: "Install dependencies py3.8"
+        condition: eq(variables['python.version'], '3.8')
+      - bash: |
+          set -e
+          source activate qiskit-aer-$(Build.BuildNumber)
+          pip install -r requirements-dev.txt
+          pip install git+https://github.com/Qiskit/qiskit-terra.git
+        displayName: "Install dependencies"
+        condition: ne(variables['python.version'], '3.8')
+      - bash: |
+          set -e
+          source activate qiskit-aer-$(Build.BuildNumber)
+          git clean -fdX
           python setup.py bdist_wheel -- -G "Visual Studio 15 2017 Win64"
-        displayName: 'Install Dependencies and Build Aer'
+        displayName: 'Build Aer'
       - bash: |
           set -e
           source activate qiskit-aer-$(Build.BuildNumber)
-          pip install dist/qiskit_aer*.whl
+          pip install -v dist/qiskit_aer*.whl
           stestr run --slowest
         displayName: 'Install Aer and Run Tests'
diff --git a/requirements-dev.txt b/requirements-dev.txt
index 6c2962f3c4..54a3d3d639 100644
--- a/requirements-dev.txt
+++ b/requirements-dev.txt
@@ -10,5 +10,5 @@ Sphinx>=1.8.3
 sphinx-rtd-theme>=0.4.0
 sphinx-tabs>=1.1.11 
 sphinx-automodapi
-jupyter-sphinx
+jupyter-sphinx;python_version<'3.8'
 stestr>=2.5.0
diff --git a/setup.py b/setup.py
index 0cc229d6a7..cb54a662d3 100644
--- a/setup.py
+++ b/setup.py
@@ -55,8 +55,11 @@ def find_qiskit_aer_packages():
         "Operating System :: MacOS",
         "Operating System :: POSIX :: Linux",
         "Programming Language :: C++",
+        "Programming Language :: Python :: 3 :: Only",
         "Programming Language :: Python :: 3.5",
         "Programming Language :: Python :: 3.6",
+        "Programming Language :: Python :: 3.7",
+        "Programming Language :: Python :: 3.8",
         "Topic :: Scientific/Engineering",
     ],
     install_requires=requirements,