How to list Azure Storage Containers and Blobs

With the new Az module, you need to do the following

Import-Module Az
$azStorageAccountName = "" # Name of your storage account 
$azStorageAccountKey = "" # Access key for your storage account
$azContainerName = "" # Container name to list your blobs
$azResourceGroupName = "" # Resource group name where storage account lives

$connectionContext = (Get-AzStorageAccount -ResourceGroupName $azResourceGroupName -AccountName $azStorageAccountName).Context
# Get a list of containers in a storage account
Get-AzStorageContainer -Name $azContainerName -Context $connectionContext | Select Name
# Get a list of blobs in a container 
Get-AzStorageBlob -Container $azContainerName -Context $connectionContext | Select Name

Not sure if this is what you want, but I am able to list containers using New-AzureStorageContext and Get-AzureStorageContainers.

$ctx = New-AzureStorageContext -StorageAccountName <name> -StorageAccountKey <key>

Get-AzureStorageContainer -Context $ctx