In TensorFlow, what is the difference between Session.run() and Tensor.eval()?

If you have a Tensor t, calling t.eval() is equivalent to calling tf.get_default_session().run(t).

You can make a session the default as follows:

t = tf.constant(42.0)
sess = tf.Session()
with sess.as_default():   # or `with sess:` to close on exit
    assert sess is tf.get_default_session()
    assert t.eval() == sess.run(t)

The most important difference is that you can use sess.run() to fetch the values of many tensors in the same step:

t = tf.constant(42.0)
u = tf.constant(37.0)
tu = tf.mul(t, u)
ut = tf.mul(u, t)
with sess.as_default():
   tu.eval()  # runs one step
   ut.eval()  # runs one step
   sess.run([tu, ut])  # evaluates both tensors in a single step

Note that each call to eval and run will execute the whole graph from scratch. To cache the result of a computation, assign it to a tf.Variable.